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^70
THE
LONDON, EDINBURGH, and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
CONDUCTED BY
SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. P.C.S.
SIR WILLIAM THOMSON, Knt. LL.D. P.R.S. &c.
AND
WILLIAM FRANCIS, Ph.D. F.L.S. P.R.A.S. P.C.S.
^' Nee araneuum sane iextas ideo mdior quia ex se flia gignunt, nee notter
Yilior qnia ex alienis libamiu at apes." Just. Lips. P6^t» lib. i. cap. 1 . Not.
VOL. XLVIIL— FOURTH SERIES.
JULY— DECEMBER 1874.
LONDON.
TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET,
Prffif«r« and Publishers to the Universiiy of London ;
•OLD BT LONGMANS, ORBSN, RBADIB, AND Dm ; KBNT AND CX>. ; 8IMPKIN, NARSnALL,
AND 00. ; AND WniTTAKBR AND CO. ; — A5D BT ADAM AND CHABLBS BLACK,
AND THOMAS CLARK, BDINBUROH ; SMITH AND SON, GLASGOW! —
H0DGB8, F08TBR, AND CO, DUBLIN: — PUTNAM, NBW
YORK: — AND ASHBR AND CO., BERLIN.
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Meditationit est perscmtari occulu; contempUtionii est adminuri
penpicua Admiratio generat qutestionem, quettio iiiTestigationem,
invesdgatio inventioiiem." — Hugo de S, Vietore,
— " Cur Spirent venti, cur terra dehiscat.
Cur mare turgescat, pelago cur tantus amaror.
Cur caput obscura Phoebus femigine coudat.
Quid toties diros cogat flagrare cometas;
Quid pariat nubes, veniant cur fulmina coelo,
Quo micet igne Iris, superos quis conciat orbes
Tam vario motu."
J. B. PinelU ad Masonimm,
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CONTENTS OF VOL. XLVIII.
(FOURTH SERIES.)
NUMBER CCCXV.— JULY 1874.
P«ge
Prof. R. Oausius on different Forms of the Virial 1
Mr. F. P. Purvis on Amsler's Planimeter 11
Prof. A. W. Wright on the Polarization of the Zodiacal Light, 13
Baron N. Schilling on the Constant Currents in the Air and
in the Sea : an Attempt to refer them to a common Cause . . 21
Mr. R. Mallet on the Tidal Retardation of the Earth's Rotation. 88
Mr. E. W. Hilgard on some points in Mallet's Theory of Vul-
canidtir 41
Mr. J. W . L. Glaisher on a New Formula in Definite Litegrals. 53
Dr. J. Rae on some Physical Properties of Ice ; on the Trans-
position of Boulders from below to above the Ice; and on
Mammoth-remains ... '. 56
Mr. P. Clowes on a Glass Cell with Parallel Sides 61
Notices respecting New Books : —
Mr. T. M. Goodeve's Prindples of Mechanics 62
The Rev. S. J. Johnson on Eclipses Past and Future, with
General Hints for Observing the Heavens 64
Proceedings of the Royal Society : —
Mr. W. Crookes on the Action of Heat on Gravitating
Masses 65
Mr. G. Gore on Electrotorsion 70
Proceedings of the Geological Society : —
His Grace the Duke of Argyll on* Six Lake-basins in
ArgyUshire 72
Prof. R. Owen on the Skull of a dentigerous Bird 73
Mr. J. W. Hulke on the Anatomy of Hypsilophodon Foxii. 74
Mr. J. Geikie on the Glacial Phenomena of the '* Long
Isknd" 74
Mr. J. F. Campbell on the Glacial Phenomena of the
Hebrides 75
Prof. P. M. Duncan on Fossil Corals from the Eocene
Formation of the West Indies 76
Mr. R. Etheridge on the Lignite-deposit of Lal-Lal, Vic-
toria, Australia 76
On the Flow of Saline Solutions through Capillary Tubes, by
Theodore Hiibener 77
On Melde's Experiment, by W. Lowery 78
On Constant Electric Currents, by M. Heine, of Halle ..... 79
On the Nature of the Action of Light upon Silver Bromide,
by M. Carey Lea, Philadelphia 80
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IV CONTENTS OF VOL. XL VI II. — FOURTH SERIES.
NUMBEE CCCXVI.— AUGUST.
Page
Mr. W. Crookes on Attraction and Eepulsion accompanying
Eadiation. (With a Plate.) 81
Mr. J. O'Kinealy on Fourier's Theorem 96
Baron N. Schilling on the Constant Currents in the Air and
in the Sea : an Attempt to refer them to a common Cause 97
Prof. M'Leod on an Apparatus for the Measurement of Low
Pressures of Ghw 110
Dr. W. H. Stone on Wind-pressure in the Human Lungs du-
ring Performance on Wind Listruments 113
Dr. W. H. Stone on the Fall in Pitch of Strained Wires
through which a Ghdvanic Current is passing 115
Mr. H. G. Madan on an Improvement in the Construction
of the Spectroscope 116
Mr. L. Schwendler on the General Theory of Duplex Tele-
graphy 117
Dr. W . H. Stone on a simple Arrangement by which the Co-
loured Eings of Uniaxial and BiaxuJ Crystals may be shown
in a common Microscope 138
Prof. W. F. Barrett on the Modification of the usual Trombone
Apparatus for showing the Literference of Sound-bearing
Waves 139
Notices respecting New Books : —
M. J. Plateau's Statique Exp^rimeutale et Theorique des
Liquides sounus aux seuleis Forces Mol^culaires 140
Mr. W. B. Birt's Contributions to Selenography 141
Proceedings of the Boyal Society : —
Dr. A. C. Bamsay on the Comparative Value of certain
Geological Ages (or groups of formations) considered
as items of Geological Time 143
Prof. O. Eeynolds on the Forces caused by Evaporation
from, and Condensation at, a Sur&ce 146
Proceedings of the Geological Society : —
Prof. W. H. Flower on the Skull of a Species of Halithn'
rium from the Bed Crag of Suffolk 163
Mr. H. Woodward on Forms intermediate between Birds
and Eeptiles .,*.,.»... 154
Mr. J. W. Hulke on the Astragalus of IguanodonManUUi;
and on a very 1r^ Saurian Limb-bone from the Kim-
meridge Clay of Weymouth, Dorset 155
On a Simple Ocular-Spectroscope for Stars, by F. Zollner . . 156
Note on the Cause of Tides, by E. J. Chapman, Ph.D., Professor
of Mineralogy and Geology in University College, Toronto. 157
On the Temperature of the Sun, by J. Violle 158
On a Peculiar Phenomenon in the Path of the Electric Spark,
by Prof. Toepler, of Graz 160
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CO!9TBNTS OF VOL. XLVIII. — FOURTH SERIES. V
NUMBEE CCCXVU.— SEPTEMBEE.
Page
Captain Abney on the Opacity of the Developed Photographic
Image 161
Mr. C. Homer on the Behaviour of certain Fluorescent Bodies
in Castor-oil 165
Baron N. Schilling on the Constant Currents in the Air and
in the Sea : an Attempt to refer them to a common Cause. 166
Prof. Challis on the Hydrodynamical Theory of the Action
of a Ghilvanic Coil on an external small Magnet. — Part I. . . 180
Prof. A. Stoletow on the Magnetization-Eunctions of various
Iron Bodies 200
Mr. A, Tylor on Tides and Waves.— Deflection Theory. (With
Three Plates.) 204
Proceedings of the Boyal Society : —
Mr. H. E. Boscoe on a Self-recording Method of Measu-
ring the Intensity of the Chemical Action of Total Day-
light 220
Mr. J. Cottrell on the Division of a Sound- Wave by a
Layer of Flame or heated Gas into a reflected and a trans-
mitted Wave 222
Mr. A. E. Donkin on an Instrument for the Composition
of two Harmonic Curves ' 223
Proceedings of the Geological Society : —
Mr. J. W. Hulke on the Anatomy of Hypsilophodon
Foxii 227
Mr. T. Mellard Eeade on the Drift-beds of the North-
west of England 227
Mr. E. D. Darbishire on a deposit of Middle Pleistocene
Gravel near Leyland, Lancashire 228
Mr. H. G. Fordham on the Structure sometimes deve-
loped in Chalk 228
Mr. £. Pinchin on the Geology of the Eastern Province
of the Colony of the Cape of Good Hope 229
Lieut. A. W. Stiffe on the Mud-craters and geological
structure of the Mekran Coast 230
On the light reflected by Permanganate of Potassium, by
Dr. Eilhard Wiedemann 231
On the Temperature of the Sun, by M. J. Violle 233
Physics of the Internal Earth, by D. Vaughan, Esq. 237
On the Conversion of Ordinary into Amorphous Phosphorus
by the Action of Electricity 239
NUMBEE CCCXVIU.— OCTOBEE.
Dr. E. J. Mills on Gladstone's Experiments relating to Che-
mical Mass 241
Dr. E. W. Davy on a very singubr Sulphuretted Nitrogenous
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VI CONTENTS OP VOL. XLVIII.— FOURTH SBRIIt.
Pace
Compound, obtained by the Action of Sulphide of Ammo-
nium on the Hydrate of Chloral 247
Dr. A. Schuster on Unilateral Conductivity 251
Lord Bayleigh on the Vibrations of Approximately Simple
Systems 258
The late W. S. Davis on a simple Method of Illustrating the
chief Phenomena of Wave-motion by means of Flexible
Cords. (With a Plate.) . . , 262
Prof. A. M. Mayer's Eesearches in Acoustics. — Xo. V 266
Prof. J. J. Miiller on a Mechanical Principle resulting from
Hamilton's Theory of Motion 274
Mr. J. O'Kinealy on a New Formula in Definite Integrals . . 295
Mr. F. Guthrie on an Absolute Galvanometer 296
Notices respecting New Books : —
The Eev. J. F. Twisden's First Lessons in Theoretical
Mechanics 298
Mr. E. Butler s Supplement to the First Book of Euclid's
Elements 300
Mr. F. Cuthbertson's Euclidian Geometry 300
Proceedings of the Boyal Society : —
Mr. J. H. N. Hennessey on Displacement of the Solar Spec-
trum 303
Mr. J. H. N. Hennessey on White liines in the Sdair
Spectrum 305
Messrs. Negretti and Zambra on a New Deep-sea Ther-
mometer 306
Proceedings of the Geological Society : —
Mr. A. B. Wynne on the Physical Geology of the Outer
Himalayan region of the Upper Punj&b, India 310
Mr. E. J. Dunn on the mode of occurrence of Diamonds
in South Africa 311
Mr. J. C. Ward on the Origin of some of the Lake-basins
of Cumberland 311
Mr. D. Mackintosh on the Traces of a Great Ice-sheet in
the Southern part of the Lake-district and in North
Wales 313
Mr. A. W. Edgell on some Lamellibranchs from the Bud-
leigh-Salterton Pebbles 313
On the Action of two Elements of a Current, by J* Bertrand. 314
On Earth-currents, by L. Schwendler, Esq 315
Experiments on the Dissipation of Electricity by Flames, bv
J. W. Fewkes \ 319
On the Stratification of the Electric Light, by M. Neyreneuf . 320
NUMBEE CCCXIX.— NOVEMBEE.
Mr. H. A . Rowland on the Magnetic Permeability and Maxi-
mum of Magnetism of Nickel and Cobalt 321
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CONTENTS OP VOL. XL VIII. — FOURTH 8BRIB8. VU
PtfC
Dr. A. Schuster's Experiments on Electrical Vibrations .... 340
Prof. ChaUis on the Hydrodynamical Theory of the Action of
a Gkdvanic Coil on an External Small Magnet. — Part U. . . 350
Sir W. Thomson on the Perturbations of the Compass pro-
duced bj the rolling of the Ship 363
Br. W. M. Watts on the Spectrum of Carbon 369
Prof. A. M. Mayer's Besearches in Acoustics. — No. V 371
Mr. C. Tomlinson on the Action of Solids and of Friction in
liberating G^ &om Solution 385
Prof. O. Eeynolds on the Surfiice-Forces caused by the Com-
munication of Heat 389
Proceedings of the Boyal Society : —
Mr. W. N. Hartley on the Chemical Constitution of Saline
Solutions 391
Mr. G. Gore <hi the Attraction of Magnets and Electric
Conductors 393
On the Temperature of the Sun, by J. Violle 395
Preliminary Notice on a new Method for Measunng the Specific
Heat of Gases, by Eilhard Wiedemann 398
On a new Formula in Definite Integrals, by J. W. L. Glaisher. 400
NUMBEE CCCXX.— DECEMBEE.
Dr. C. B. A. Wright on the Relations between Affinity and
the Condensed Sjrmbolic Expressions of Chemical Facts and
Changes known as Dissected (Structural) FormulaB 401
Prof. Challis on the Hydrodynamical Theory of the Action of
a Gblyanic Coil on an external small Magnet. — Part III. . . 430
Prof. A. M. Mayer's Besearches in Acoustics. — No. V 445
Lord Bayleigh on a Statical Theorem 452
Dr. W. M. Watts on Carbon-Spectra 456
Mr. J. W. L. Glaisher on the Problem of the Eight Queens . . 457
Notices respecting New Books : —
The Hon. Sir W. E. Grove's Correlation of Physical
Forces 467
Mr. W. G. WiUson's Elementary Dynamics 471
Proceeduigs of the Eoyal Society : —
Dr. W. Huggins on the Motions of some of the Nebul©
towards or from the Earth 471
On the Intensity of the Light reflected from Glass, by Dr. P.
Glan 475
Pohurization of the Plates of Condensers, by A. S. Thayer . . 478
On Electrical Currents accompanying the non-simultaneous
Immersion of two Mercury Electrodes in various Liquids,
by G. Quincke 479
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VIll CONTENTS OF VOL. XLVIII. — FOURTH SERIES.
NUMBER CXX^XXI.— SUPPLEMENT.
Ptge
M. H. Herwig : the Heat-conducting Power of Mercury in-
dependent of the Temperature 481
Prof. J. Lovering on the Mathematical and Philosophical
State of the Physical Sciences 493
Mr. B. H. M. Bosanquet on Temperament, or the Division
of the Octave 507
Mr. S, Sharpe on Comets and their Tails 512
Prof. A. M. Mayer s Researches in Acoustics. — No. V 513
Mr. F. Guthrie on an Absolute Galvanometer 526
Notices respecting New Books : —
Mr. D. D. Heath's Elementary Exposition of the Doc-
trine of Energy 527
Mr. B. A. Proctor's Transits of Venus 529
Dr. W. Huggins's Approaching Transit of Venus 529
Proceedings of the Boyal Society : —
Prof. O. Beynolds on the Befraction of Sound by the
Atmosphere 530
Mr. T. Grubb on the Improvement of the Spectroscope. 532
Drs. Stewart and Schuster's Preliminary Experiments on
a Magnetized Copper Wire 535
Proceedings of the G^ologicil Society : — '
Mr. J. W. Judd on the Secondary Bocks of Scotland . . 541
Mr. A. W. Waters on Possils from Oberburg, Styria . . 545
On the Cosmic Dust which falls on the Surface of the Earth
with the Atmospheric Precipitation, by A. E. Nordenskiold. 546
On the Passage of Gases through Liquid Films, by Dr. F.
Exner 547
Index 548
ERRATUM.
Page 203, note f", line ^A^for liniiteil r*ff<iiClo»ed.
PLATES.
L lUuatratiTe of Mr. W. Crookes's Paper on Attraction and Repulsion
accompanving Radiation.
II.. III., and iV. Illustrative of Mr. A. Tylor's Paper on Tides and Waves.
V. Illustrative of Mr. W. S. Davis's Paper on a simple Method of Illus-
trating the chief Phenomena of Wave-motion by means of
Flexible Cords.
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THE
LONDON, EDINBURGH, and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
JULY 1874.
I. On different Forms of the Virial. By R. Clausius*.
MY theorem of the virial has already given rise to some
discussions on the forms which the virial can assume.
I myself, in my first memoir relative to itfi indicated that when
the movable points partly exert forces upon one another, and
partly are acted on by forces from without, the virial can be
analyzed into an internal and an external, and gave their forms
for certain frequently occurring cases. Yvon Villarceau subse-
quently [Comptes Rendus, vol. Ixxv.) effected other transforma-
tions of the equation relating to it, especially by resolving the
total motion of the system of material points into the motion of
the centre of gravity and the relative motions of the individual
points about the centre of gravity, and referring the equation to
each of these two constituents singly. Prompted by this, in a
note published in the same volume of the Comptes Rendus I
added a series of further transformations. As, however, in that
brief note results only, without demonstrations, could be com-
municated, and those but imperfectly, a more connected treat-
ment of a subject so important in itself will not be void of
interest.
1. The simplest form of the equation in question is the fol-
lowing. If m denotes the mass of a material point which is in
stationary motion together with other material points, of, y, z
its rectangular coordinates at the time /, and X, Y, Z the com-
* Tianslated from a separate impression, communicated by the Author,
from PoggendorflTs Annalen, Jubelband, p. 41 1.
t Bertchie der Niederrhein. Gesellsch. fur Natur- u. Heilkunde, June
1870; Phil Mag. S. 4. vol. xl. p. 122 ; Pogg. Ann. vol. cxli. p. 124.
PhiL Mag. S. 4. Vol. 48. No. 315. July 1874. B
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2 Prof, R. Clau8iu8 on different Forms of the ViriaL
ponents of the force acting upon it^ then
or, if (as will always be done in the following) the first differen-
tial coeflScient according to time be indicated by affixing an
accent^
-;r«=:-^X^+5-^ (1«)
From this results, indicating mean values by drawing a hori-
zontal stroke above : —
'^¥'=-\y^x (2)
If we name the quantity ^ a^^ the vis viva with respect to the
^-direction, and the quantity "" 5 ^ ^^^ virial relative to the
a?-direction, since the x- is any direction we please, the meaning
of the equation can be expressed thus : — For each freely movable
point f the mean vis viva relative to any direction is eqital the virial
relative to the same direction.
If we form for a point the equations relative to the three di-
rections of its coordinates and add them up, we get (r denotin<^
the velocity of the point, and / its distance from tlie origin of
the coordinates): —
J.--|(Xx + yy + Z.) + ^^P. ... (3)
If, further, we denote by L the component, in the direction
of /, of the force acting on the point, and i*eckon it positive fi-om
the origin of the coordinates onward, the equation (as is readily
seen) becomes: —
2*'=2^'+4-rfl* (*)
It is obvious that these equations, which are valid for each
individual point, can be extended by simple summation to the
entire system of points. We thus obtain : —
-. m « 1 -., , 1 d^XmP
2.jr»=22L/+^-^^-5- (7)
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Prof. R. Clausius on different Forms of the ViriaL 3
In the formation of the mean values, in all these equations
just as in (1), the last term on the right-hand side falls away ;
and the expression then remaining on that side represents the
virial.
2. The first method of transformation of these equations is
based on the fact that when the points are acted on by forces of
different sorts which we wish to consider singly, the force-com-
ponents can be separated into as many summanda as the kinds
of force that are to be distinguished, whereby the virial is divided
into just as many parts.
If, for instance, the above-mentioned distinction be made be-
tween the forces which the points of the system exert on each
other, and those which act upon the system from without, and
this be denoted by the indices i and e, we can put X = X, -f X^;
and the same holds for the components Y, Z, and L. It is
readily seen how the above equations are changed by the inser-
tion of these sums. Equation (6), for example, thereby changes
into
^is?- ^^)
When more special assumptions are made concerning the
nature of the forces, the expressions also take more special forms,
of which I will briefly cite two which are exhibited in my first
memoir. When, namely, the internal forces consist of reciprocal
attractions or repulsions^ which, according to any law, depend
on the distance, so that for two points whose distance is r the
force (which as an attraction is reckoned positive, and as a repul-
sion negative) can be represented by a function ^(r), we can put
-\l.{7.f + Y,y^Z,z) = \lr<i>{r), ... (9)
in which the sum on the right-hand side refers to all combina-
tions of two mass-points each. When the system of points is
further considered as a body on which the only external force
acting is a symmetrical pressure/? normal to the surface, we can put
-|2(X,^+Y,y + Z,r)=|pV. .... (10)
in which V denotes the volume of the body.
3. Another mode of transformation depends on the separation
of the coordinates of the points into summanda.
To this belongs the transformation effected by Yvon Villar-
ceau. If, namely, besides the fixed systems of coordinates, we
B2
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4 Prof. R. Clausius on different Forms of the Virial.
introduce a movable system having for its origin the centre of
gravity of all the material points^ and parallel to the fixed sy stem,
and if we name the coordinates of the centre of gravity in rela-
tion to the fixed system Xc, y^ ^o ^^^ the coordinates of any one
of the material points in relation to the movable system ^, 77, ^,
then is
^=^c+f, y-Vc^Vy ^='8'r+(;
If we now form the equation
and consider that we may put
we gct^ if M denotes the total mass of all the material points^
consequently the sum Sm, the equation
2wa^=Ma:J + 2wf« (11)
In precisely the same manner we obtain
2W*=M;r'J + 27n^« (12)
Finally, the mere substitution in SXj? of a?^ + f for the coor-
dinate X, Xp denoting the sum 2X, gives
2Xa- = X,^e + 2Xf (13)
If now we form for the centre of gravity the identical equation
which for a single material point has served for the derivation
of (1), viz.
2 <//« ~\dt) '^''' dt*'
which, after multiplication by ^,canbe writtcD thu.4.
and suppose herein
3
we then obtain
** rf?^^'"5?''^^^^"
2^'- 2^*'+ 4^r« (^*)
With the aid of this equation in conjunction with (11), (12),
and (13), the following equation can be immediately derivtd from
(5):-
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Prof. R. Clausios on different Forms of the VirtaL 5
2^r»=-^2Xf+l^. . . . (15)
All the equations above derived for the j?-direction, of course
bold good in a corresponding manner for the other two direc*
tions of coordinates ; and when each three equations thereby
arising are added together^ a new system of equations is ob-
tained. In order to write these conveniently^ let us introduce
the following symbols. We will nanie the distance of the centre
of gravity from the origin of the fixed coordinates /<.; and the
distance of a mass-point from the centre of gravity, \. Let the
velocity of the centre of gravity be called Vc, and the relative
velocity of a mass-point about the centre of gravity, consequently
the quantity \/f 4-»/*+|^*, be called w. Further, of the force
whose components in the coordinate-directions are X^, Yc, Z<.,
the component in the direction of /« may be denoted by 17^ ; and
of the force acting on a mass-point, let the component in the
direction of X be denoted by A. Then the equations will be
written as follows : —
2w/«=M/J-f-2mX«, (16)
ltnv^=Mvl + l.mw^, (17)
2L/=LA-h2xV\, (18)
*^.« Iri^^^i^) 119)
^t.,= ^LA+4 ^^. .... (19)
2fu;'=l2AX+^^'|p^'. •. . . (20)
4. We will now turn to the kind of transformation which I
communicated in the Comptes Rendus, and which depends on the
introduction into the formulee of the mutual distances and rela-
tive velocities of each two material points.
Firsts if V and fi represent any two of the indices 1, 2, 3, &c.,
and accordingly m^ and m^ are any two of the given mass-points
with the coordinates Xy, yy, Zy and ^^ y^, z^^y we can form, corre-
sponding to the above, the following identical equation,
or, differently arranged and written.
Digitized by VjOOQIC
6 Prof. R. Clausius on different Forms of the ViriaL
which by introducing the force-components is changed into
Just such equations hold for the other two coordinate-directions ;
and we will add up these three equations. Therein the distance
between the two points shall be denoted by r ; and their relative
velocities, consequently the quantity
we will call u. Lastly, of the forces acting on the mass-points
m^ and m^, let the components which fall in the direction of r
be denoted by B^ and R^, and at the same time let the direction
of force from each point to the other point be reckoned positive.
We can then put : —
Xy{x^—Xy) +Y^(y^— y^) +Z^(j2r^-5r^) = R^,
X^(^,,-4?^) + Y^yr-y^) + Z^(j8r,--r^)=R^r.
Accordingly the equation resulting from the above-mentioned
addition takes the following form : —
Into this we will introduce another simpUfying symbol, putting
the equation will then read : —
„.=a,+^) (24)
Multiplying this equation by ^—^ and extending it to the
entire system of points, wc get
A2«^^„«=_l-2m^^»,+ _l.^^', . (2J)
wherein the three sums refer to all the combinations of two each
of the given mass-points.
5. Between the sums which occur in this equation and the
sums previously considered, there are simple relations, which
can be discovered by means of a general formula of transforma-
tion. For, besides the masses tw,, 7n^ . . . m„, given two other
groups of quantities belonging to them, which shall provisionally
Digitized by VjOOQ IC
Prof. R. Clausios on different Farms of the ViiioL 7
be denoted hj p^,p^ .../>« and jj, y^, . . . j«, then the following
identical equation holds : —
2m^^(/?^--/?^)(gf^— gr^)=2m2inpj— SmpSmj; . . (26)
in which the sum on the left-hand side refers to all combinations
of two masses each^ while the sums on the right-hand simply refer
to all the masses. A conviction of the correctness of the equation
can be obtained by carrying out the multiplication on the left-
hand side^ and suitably arranging and collecting the terms then
contained in the sum. We will now apply this equation to our
case by attributing successively different significations to the
quantities p and q.
First let ua prxtp^q^x; the result is: —
Xm^f^{x^^x^^='ZmS,ma^'- (2i?wr)*=M2mar'— M*a?J.
We then fxitp=q=a^, and obtain in a corresponding manner
2f7i^^(a/, -a^^)«=M2ma/«-.M«a?';.
Lastly, we put /;= — and q^x; then comes
2m,»i^(~ - ^-^)(a?,-ar^)=2m2Xa?-2X2in^
=M2X5?-MXcare.
Just such equations are valid for the other two directions of
coordinates ; and if we form the sum of each three belonging to
one another and divide it by M, we obtain the equations ex-
pressing the relations sought, namely : —
j^2m,7n^r«=2m/«-M/2, .... (27)
^2m,7n^u«=2mt^-MrJ, .... (28)
^2^^»r=2L/-Le/e (29)
Combining these with equations (16), (17), and (18), we get
the following very simple equations : —
^2m,m^r« = 2»«\«, (80)
jg-2m^^tt'=2mi(;*, (31)
^2m,m^»r=2A\ (82)
Digitized by VjOOQ IC
8 Prof. R. Clausius on different Farms of the Firiat.
It scarcely needs to be meotioDed that in equations (8), (14),
(15), (19), (20)^ and (25)^ as well as in the earlier corresponding
equations, with the formation of mean values the last term
(which is a differential coefficient according to time) drops out,
and the terms then remaining on the right-hand side are forms
for virials, the special signification of which is readily seen in the
individual cases.
6. Having thus far been occupied in introducing special quan-
tities of various kinds for the determination of the virial^ we will
finally derive some equations which, in relation to the variables
to be employed, are perfectly general.
Given any variables serving to determine the positions of the
points, and denoted by q^, q^ q^ &c., then the coordinates of
the points, and all the quantities determined by them, are to be
regarded as functions of these general variables. The velocities,
and the quantities determined by them, can accordingly be re-
presented as functions of these variables and of their coefficients
of differentials according to time. Let us now assume that the
forces acting in our system have a force-function or ergal U, we
can treat this as a function oi q^, q^^ q^ &c., and at the same
time the vis viva T of the system as a function of ^„ q^ q^ &<;.
and ^,, 9',, q'of &c. Between these two functions there subsists,
according to Lagrange, the following equation,
in which the sum refers to the variations of all the variables
9v 99> 9s9 &c* If* fo** abbreviation, we introduce the symbols
Pv P2f P9> ^'» ^^^ f^^
dT
^ P'-W.' ^''^*
V signifying any one of the indices ^, v s> ^^^ preceding equa-
tion becomes : —
SU
=X[^-j/)Sq. .... (85)
Besides, according to Lagrange, the following easily derived
equation holds for the vis viva T : —
T=|2;»?' (86)
If wc now differentiate according to time the product p^, q^,
we have
rf(M.) =p^,^,^qj,,
Digitized by VjOOQ IC
Prof. R. Clausius on different Forms of the ViriaL 9
whence results
;'y.= -?y,+ ^ (37)
Herein^ (orp^,, we can put an expression to be obtained from
(85). For this purpose we will write (35) in the following
form: —
2f «?=2(^-p'>. . . . (88)
If now the variables q^, q^ q^ &c. are each independent of the
others^ their variations are also independent of each other, and
the equation which holds for the sum of all the terms must also
hold for each term singly ; we consequently obtain
dq, dq^ ^ -^
or
If we insert this expression for j&^ in equation (37), after mul-
tiplying it by \, we get
2^'^" 2 dq^ ^'^ 2 dt' ' ' • • ^^^>
and when we form the sum of all the equations of this kind, we
obtain, in accordance with (36),
1 rf(U-T) \dtpq
^"2^ dq ^^% dt ' • • • ^^^^
These equations (40) and (41) are two new equations represent-
ing generalizations of equations (1) and (6).
By forming the mean values, new forms of virial-cxpressions
can be deduced from them. In the first place, the expression
for the total virial resulting from the last equation is : —
2^ dq *+2'^r"
In regard to the last term in this expression a special remark
must be made. ITie variables q.^ q^, S's > • • • s^^^ve for the deter-
mination of the positions of the movable points; and, con-
versely, the values of the variables can be determined from the
positions of the points. This latter determination, however,
may take place in two ways. It may have but one meaning —
which is the case for right-line coordinates, the distances of the
movable points from one another or from fixed points or the
centre of gravity, and for the trigonometrical functions of the
Digitized by VjOOQ IC
10 Prof. R. Clausius on different Farm of the Virial.
angles made by such right lines; or it may be ambiguaui —
which is the case with the angles themselves^ since to one direc-
tion an infinite number of angles belongs which differ from one
another by 27r. In the former case l,pq is a quantity the value
of which, with a stationary motion, varies only within certain
limits , and accordingly the mean value of the differential coe£S-
cieut, taken according to time, of this quantity may at once be
regarded as vanishing and be omitted from the above expres-
sion. In the latter case, on the contrary, the mean value of that
differential coe£Bcient does not necessarily vanish, and hence it
must remain in the expression for further consideration.
Should the variables q^, g^, g^, &c. not be all independent,
but connected with one another by certain condition-equations,
then we can, notwithstanding, obtain equations similar in form
to (40) by employing Lagrange's indeterminate coefficients.
Let, namely,
&c.
be the given condition-equations, we form instead of (38) the
following equation,
where p, o-, &c. are indeterminate coefficients ; and this equation
is to be resolved, in the usual way, into as many partial equa-
tions as there are variations. The partial equation correspond-
ing to the variable q^ is then
dV rfT I ^ d4>^ dit .
dq^ dq, "^"^ "^dq^ dq^
whence results
rf(T--U) d^ rff
(42)
By the insertion of this value of j/^ equation (87) is changed
into
^"^^ L dq^ ^dq^ dq^ ^^^ dt ^ ^
As many equations of this form are obtained as the given vari-
ables 9„ ^9, ^3, &c.; and the work can be supplemented by eli-
minating from them the indeterminate coefficients.
It is thus shown in a general way how the equations which
Digitized by VjOOQ IC
Mr. Y. P. Parvis on Amsler's Plardmeter. 11
serve for the determination of the virial can be formed with the
employment of any variables; and with this I think I may on
the present occasion be satisfied^ without entering upon special
applications of the equations — which may be of very various
kinds, and^ hence, would lead to extended discussions.
II. On Amskr^s Plmimeter. By F. P. Purvis, Esq.*
THE following is a simple and thoroughly general explana-
tion of the action of this perplexing little instrument.
Suppose, for simplicity and greater generality, that the instru-
ment consisted simply of the straight bar A B, of length /, car-
rying a pencil at each end, A and B ; and suppose any lines A a,
B b were traced out by these pencils : we will consider how the
area A a ^ B may be expressed in terms of / and the motion of
some point in the line AB.
Let the motion from AB to ayS represent an elementary
motion of the bar, the centre of it C moving from C to 7, and
the bar turning about y through the angle dO ; let rfnaa the
normal distance from y to A B ; this motion may be considered
to take place in two parts : — Ist, the motion of A B parallel
to itself into the position xy ; 2nd, the motion of AB about its
centre into the position a/S; the required area A a ^ B is, in
this elementary motion, equal to the area AxyB {^Idn), since
the area 7 a x = the area 7 jS y, and the areas A aw and B^y
are negligible with respect to Idn, being the product of two in-
finitesimal quantities, while Idn is the product of one infinitesi-
mal quantity (comparable with each of the two just mentioned)
and the finite quantity /.
Integrating for the whole area A a & B, we see that it is ex-
pressed by In, where n is the travel of the point C normally to
the bar A B.
Now we may obtain that normal motion n by centring a
wheel on the bar at C, free to revolve in the plane at right angles
* Communicated bv the Author.
Digitized by VjOOQ IC
12
Mr. r. P. Purvis on Amsler's Planimeter.
to A B^ and resting at its circumference on the paper. That it is
given by the circumferential motion of this wheel may be seen
by considering again the elementary motion of the bar from A B
to « ^ : while the bar moves from AB to ar j^, the wheel turns
through the normal distance from 7 to AB; while the bar
turns about the point y, the wheel remains stationary.
If instead of centring the wheel at C we centre it at any
other point J), distant m from C, its circumferential travel for
the elementary motion will be the normal from z to A B( = dn)
--mdO, and for the whole motion from A B to a ^ will be n-^mO,
where ^= the inclination of a & to A B.
If a retrograde motion be now given to the instrument, bring-
ing it into the position c/b', the product nl will still equal the
area included between AaJ^Bb b\ and the two straight lines
A B and Jlf, part of that area being, in the case shown, negative ;
nl=iAaa! IB-^lbb^ If instead of allowing B to take any path
bV ift constrain it to move only along the line already traced,
while A traces out a new line a a, the negative area will be nil,
and the product nl will equal the area Aaalb^B, If this motion
be continued, B being always kept in the path A^B until AB
occupies its initial position, the product nl will equal the area
A a a' A, whatever be the nature of the line Bbf b. Also for the
whole motion ^=0; so that the circumferential travel of the
wheel at D = n, entirely independently of the value of m.
Digitized by VjOOQ IC
On the Polarization of the Zodiacal Light. 1 3
Now in Amsler'a planimeter the point B is constrained to
move in the arc of a circle, while the pencil A is traced ronnd
the contour of the required area ; this is simply a limitation of
the more general case taken above. Also the wheel whose
travel is measured is placed away from the centre of the bar C,
and indeed on the opposite side of B ; but, as we have seen, its
position, so long as its centre is oa the line AB, is quite imma*
terial, its motion in the aggregate being the same as if it were
placed at G.
In the planimeter the length / is capable of variation ; so that,
by setting it differently, the same graduation on the wheel will
give areas in different units, the unit of area being always Ix
the circumferential travel of the wheel required to alter its read-
ing by unity.
III. On the Polarization of the Zodiacal Lif/ht.
By Professor Arthur W. Wright*.
FROM the published accounts of observations upon the zo-
diacal light, it would seem that few attempts have as yet
been made to determine whether or not any portion of the light
is polarized, and the results thus far obtained leave the question
still undecided. The few notices that can be found in the scien-
tific journals, though uncertain and contradictory, tend to the
view that it is either not polarized at all, or that the proportion
of polarized light is so small as to render its detection a matter
of excessive difficulty. It may be observed that most of the
observations giving negative results appear to have been made
with Savart's polariscope ; but with an instrument which ab-
sorbs so large a proportion of the light as a Savart, the amount
of polarization necessary to render the bands visible increases
very greatly as the light becomes fainter, and especially so as it
approaches the limit of visibility. Numerous attempts have
been made by the writer to detect traces of polarization with a
Savart, but never with the slightest result, excepting that on one
especially clear evenings when the zodiacal light was unusually
distinct^ the bands seemed to be visible by glimpses, on the
utmost exertion of visual effort. The observation was so un-
certain, however, that it was considered worthless.
Nearly a year ago a series of observations was begun, in the
course of which a variety of apparatus were employed, by the use
of which it was hoped polarization might be detected, either, as
in the Savart, by bands or other variations in the brightness of
parts of the field, or as with the double-image prism, the NicoPs
* From Silliman's American Journal, May 1874.
Digitized by VjOOQ IC
14 Prof. A. W. Wright en. the Polarization
prism^ or a bundle of glass plates set at the polarizing angle> by
a diminution of the brightness of the object itself. None of
them, however, gave results of any value. In resuming the
study of the subject some months later^ the attempt was made
to find a combination which should give a large field of view,
and which, while absorbing as little light as possible, should in-
dicate the pre^nce of even small proportions of polarized light,
by sufficient variations of intensity to render it available with
the faintest visible illumination.
A Savart in which the tourmaline was replaced by a Nicol,
though possessing almost perfect transparency, was found to
give too small a field of view, and bands too faint to render it
of any service. Amother instrument was constructed on a plan
similar to that adopted by Mr. Uuggins in observations upon
Encke*s comet*, by placing a large double-image prism in the
end of a tube 18 inches long, the other end of which had a
square aperture a little more than an inch in diameter. The
distance was so adjusted that the two images just touched with-
out overlapping. This seemed to promise well ; and on using
it diflferences of intensity were perceived which indicated polari*
zation in a plane passing through the sun. Two defects, how-
ever, are inherent to this mode of investigation : — one, that if
the field is not of uniform brightness thi-oughout, the brighter
side of one image may be juxtaposed to the fainter side of the
other, thus giving rise to false conclusions ; another is the un-
equal sensibility of diflFerent parts of the i*etina. In consequence
of this, the one of the images directly viewed seems always the
more obscure, and the true relation of their intensities can only
be found by indirect vision, the eye being turned to some point
in the median line of the images. Although when used with
the observance of the necessary conditions this instrument is
capable of ginng trustworthy indications, it was soon abandoned
for a better.
Among the polariscopic apparatus belonging to the physical
cabinet of Yale College, a quartz plate was found, cut perpendi-
cularly to the axis, and exhibiting by polarized light an unusual
intensity of colour. It is a made, the body of the plate consist-
ing of left-handed quartz, through which passes somewhat ex-
centrically a band of right-handed quartz, 6*5 millimetres in
breadth. This band is not bounded by sharp lines of division
on the sides, but by intermediate strips {b, o in the figures),
about 2 millimetres in breadth, which are of different structure,
and are apparently formed by the interleaving of the strata of
the two portions at their edges. In the polarizing apparatus
these strips simply vary from bright to dark, without marked
♦ Phil. Mag. S. 4. vol. xliii. p. 382.
Digitized by VjOOQ IC
of the Zodiacal Light, 1 5
appearance of colour. Placed between two Nicols, the plate has
the appearance represented in the accompanying figures^ which
are drawn of full size. When the corresponding diagonals of
Fig. 1. Fig. 2.
the Nicols are parallel, or nearly so, the bands are white upon
a deep reddish- puq)le ground, as shown in fig. 1 ; with the
Nicols crossed, the bands are dark upon a light greenish-yellow
background, as represented in fig. 2. Turning one of the
Nicols 45° in one direction, the observer sees the central band
a intensely blue upon a yellow ground ; turning in the other
direction, a bright yellow upon a dark blue; and intermediate
positions give the usual varying tints. Examined with one Nicol
and unpolarized light the plate is perfectly colourless, and shows
no trace of its heterogeneous structure.
The quartz plate was placed in one end of a tube, large enough
to admit its full size very nearly, and 11 inches in length.
This was found better than a shorter one, as the bands are most
easily seen when not nearer the eye than the limit of distinct
vision. In the other end was placed a good-sized Nicol ; and
the tube was provided with a joint, so that the latter could be
easily turned. Thus mounted the plate and Nicol form a po-
lariscope of extraordinary sensibility, with faint light far excel-
ling the best Savart, and even with strong light somewhat
superior to it. The instrument is especially suited for the detec-
tion of small degrees of polarization, and the examination of
very faint lights. The occurrence of the narrow strips is pecu-
liarly advantageous, as with very feeble illumination they appear
bright upon a dark ground, or the reverse, and are thus more
easily seen. The efficiency of the instrument is further increased
by the comparatively large field of view and the perfect trans-
parency of the whole combination.
As a test of its delicacy may be mentioned that when a glass
plate is laid upon the window-sill, and the light of the sky in a
clear moonless night, after reflection from it, is viewed through
the instrument, both bright and dark bands are easily seen, the
former appearing surprisingly luminous in contrast with the
Digitized by VjOOQ IC
16 Prof. A. W. Wright on the Polmisalion
darkened field. The plane of polarization is easily determined
with it^ since when the bright bands appear, as iu fig. 1, the
longer diagonal of the Nicol is in that plane ; when the bands
are dark, the plane of polarization is parallel to the shorter
diagonal.
On the completion of the instrument the first favourable op-
portunity was iinproved to test its efficiency upon the zodiacal
light it was almost immediately found to indicate the exist-
ence of light polarized in a plane passing through the sun.
The bands were fainter than had been expected, and at first were
overlooked. More careful attention, however, and the obser-
vance of suitable precautions established their presence beyond
a doubt. The observations were made in a room in the upper
floor of one of the college buildings, the windows of which look
toward the south-west, and command a clear view nearly to the
horizon. The room during the observations received light only
from the sky, which sufficed to render objects dimly visible. After
being exposed only to this dim light for ^ih^exi or twenty minutes,
the eye became sufficiently sensitive for observation. This was
a very necessary precaution, as a moment's exposure to a bright
light rendered the eye unfit for delicate discrimination of lumi-
nous intensities for a long time. The Nicol of the instrument
was now turned round and round, so that no previous know-
ledge of its position relatively to the bands of the quartz plate
might intiuence the judgment as to their character and position.
On looking through the tube at the zodiacal light, and turning
the whole instrument slowly round, it was possible to find a
position where the bands could be seen, and their nature and
direction determined. They could rarely be seen steadily by
direct vision, and then only for a few moments, as the excite-
ment and fatigue of the eye consequent upon the straining
effort of vision soon rendered the field a confused blur. Allow-
ing the eye to rest a few minutes, also on turning it obliquely
and rapidly directing it to different parts of the field, and espe-
cially by suddenly bringing it to focus upon* the quartz plate,
the bands could be distinctly seen, and their direction fixed with
a good degree of certainty. On the clearest nights the brightest
bands (6, b, fig. 1) were seen without much difficulty, the broad
dark band (a), corresponding to an inclination of 45^ in the
Nicol, less easily, and the dark bands (6, A, fig. 2) by glimpses.
After determining, by repeated observations, the angle made by
each of the bands with some fixed line, as the axis of the zodiacal
light, or a line nearly parallel to it drawn between two known
stars, the position of the plane of polarization was found, by
means of light from a gas- flame reflected from a sheet of white
paper placed in a suitable position, or by observing the position
Digitized by VjOOQ IC
of the Zodiacal Light. 17
of the Nicol. The resalts of the numeroad observations of dif-
ferent evenings were entirely concordant^ and showed that the
plane of polarization pasaes through the sun^ as nearly as it was
possible to fix its direction. In no instance when the sky was
clear enough to render the bands visible did their position^ as
determined by the observations, fail to agree with what would
be required by polarization in a plane through the sun. Not
the slightest trace of bands was ever seen wl^n the instrument
was directed to other portions of the sky.
These observations, for the most part, were made in the ten
days preceding new moon in January and February of the pre-
sent year. During this time there was an unusual number of
clear nights, with the atmosphere cold and still. A few good
evenings in March and April also were improved in verifying
the results previously obtained. The absence of the moon, and
the distance of any of the brighter planets and stars from the
field of observation, removed all uncertainties from these sources.
As the instrument was directed to points from 30 to 40 or even
more degrees from the sun, the polarization could not have pro-
ceeded from faint vestiges of twilight. That it did not arise by
reflection of the zodiacal light itself in the atmosphere, or from
atmospheric impurities, is shown both by its amount and the fact
that it was always most easily discernible on the clearest nights.
The next step was to determine what percentage of the light
is polarized. The failure of the common apparatus to detect it
shows that the proportiou is not large ; but it must be recollected
that for a light so very faint much greater differences of inten-
sity are imperceptible than in cases where the luminous intensity
is greater. The determinations were made as follows. A bundle
of four pieces of excellent plate glass was placed vertically at the
centre of the horizontal divided circle of a DeleuiPs goniometer,
the telescope of which was replaced by the polariscope used in
the preceding observations. The latter was so placed that iu
axis was perpendicular to the surface of the bundle when the
index of the goniometer was at zero. With the instrument thus
adjusted no bands are seen when unpolarized light is passed
through it ; but on turning the glass plates bands become visible
corresponding to polarization in a vertical plane. The amount
of the light polarized by refraction through four glass plates at
different incidences has been calculated by Professor W. G.
Adams* for intervals of 6^ from 10° to 70°, and at 72°. Taking
the values given in his Table for crown glass ()b(=sl*5), those for
intermediate angles are readily determined by interpolation, or
graphically. The latter method was employed, a curve being
* Monthly Notices of the Royal Astronomical Society* March 10, 1871,
p. 162.
Phil. Mag. S. 4. Vol 48. No. 815. July 1874. C
Digitized by VjOOQ IC
18 Prof. A. W. Wright on the Polarization
drawn representing all the values in the Table. The results
given in the Table correspond very well with those obtained by
Professor Pickering*, who verified his values experimentally,
and showed that the deviation from theory in the case of four
plates only becomes perceptible above 65^. As Professor Pick-
ering used the value /a =1 '55, the numbers in his Table are
slightly greater than those used in constructing the curve from
Professor Adams's Table.
The determinations were made by observation of the percent-
age necessary to render the bands visible with the same distinct-
ness as in the zodiacal light. A set of experiments were made
with light from the clear sky in a moonless night, the instrument
being directed to one of the brightest points of the galaxy,
where the light, though less bright than that of the zodiacal
light, did not very greatly diflFer from it in intensity. The glass
plates being turned until the bands had the same degree of di-
stinctness as in the previous observations, the mean of several
observations gave as the polarizing angle 41^, corresponding to
a percentage of 20*5. This value, on account of the inferior
brightness of the light compared, is somewhat too large, and
may be taken as an upper limit.
To find a lower limit and, at the same time, an approximate
value, light reflected from a nearly white wall with a dead sur-
face was employed. The point observed with the instrument
was so chosen as to be equally distant from two gas-flames so
f>laced that the planes through them and the axis of the po-
ariscope were at right angles, thus giving light entirely free
from polarization. The flames were now turned down equally,
so that the field had, as nearly as could be estimated, the same
brightness as it had with the zodiacal light. A small scratch
upon the quartz plate, which could just be seen by the light of
the latter, served as a means of control in adjusting the inten-
sity. The experiments being conducted as before, gave, as the
mean of numerous determinations, the angle 86^*6, correspond-
ing to a proportion of 16 per cent.^ which is probably not far
from the true value of the amount sought. Another, in which
the light was made perceptibly brighter than that of the zodiacal
tract, gave for the angle 28^*5, and a percentage of 9*4, which
is certainly too small. We may safely take 15 per cent, as near
the true value.
The fact of polarization implies that the light is reflected,
either wholly or in part, and is thus derived originally from
the sun. The latter supposition is fully confirmed by various
spectroscopic observations, of M. Liais f. Professor C. Piazzi-
* Silliman's American Journal, S. 3. vol. vii. p. 102.
t Comptes Rendus, 1872, vol. Ixxiv. p. 262.
Digitized by VjOOQ IC
of the Zodiacal Light. 19
Smyth 'i'^ and others^ which show that the spectram is continuous,
and not perceptibly di£ferent from that of faint sunlight. The
writer has also made numerous observations with a spectroscope
specially arranged for faint light, of which an account will be
published hereafter, and which lead to the same conclusion. It
may be mentioned further that a particular object in these ob-
servations was to determine whether any bright lines or bands
were present in the spectrum, or whether there is any connexion
between the zodiacal light and the polar aurora ; and the results
give, as an answer to the question, a decided negative. This is
important here, as excluding from the possible causes of the
light the luminosity of gaseous matter, either spontaneous or
due to electrical discharge. The supposition that the light is
reflected from masses of gas, or from globules of precipitated
vapour, is not to be entertained, since, as Zollnerf has shown,
such globules in otherwise empty space must evaporate com-
pletely, and a gaseous matter would expand until its density
became far too small to exert any visible effect upon the rays of
light.
We must conclude, then, that the light is reflected from mat-
ter in the solid state — that is, from innumerable small bodies
revolving about the sun in orbits, of which more lie in the
neighbourhood of the ecliptic than near any other plane passing
through the sun. Although such a cause for the zodiacal light
has often been assumed as probable, no satisfactory proof of it
has hitherto been found ; and the establishment of the fact of
polarization was necessary to its confirmation, since spectroscopic
appearances alone leave it uncertain whether the matter is not
self-luminous.
If these meteoroids, as there is no good reason to doubt, are
similar in their character to those which have fallen upon the
earth, they must be either metallic bodies, chiefly of iron, or
stony masses with more or less crystalline structure and irre-
gular surfaces. If we accept Zollner's conclusion that the
gases of the atmosphere must extend throughout the solar sys-
tem, though in an extremely tenuous condition in space, the
oxidation of the metallic meteoroids would be merely a question
of time. They would thus become capable of rendering the
light reflected from them plane-polarized ; and the same effect
would in any case be produced by those of the stony character.
In order to ascertain whether the proportion of polarized light
actually observed approached in any degree what might be ex-
pected from stony or earthy masses of a semicrystalline cha-
racter with a granular structure and surfaces more or less
* Monthly Notices of the Royal Astronomical Society, June 1872, p. 277*
t l/«6er die Natur der Cometen, p. 79 ^t seq.
C2
Digitized by VjOOQ IC
20 On the Polarization of the Zodiacal Light*
rough, a large number of substances possessing these charac-
teristics were subjected to examination with a polarimeter. For
this purpose the apparatus already described was employed,
there being added to it a support for the object, with a hori-
2ontal circle for determining the azimuths in placing the object
and the light. The substances examined had approximately
plane surfaces, which were placed vertically and so that the
normal, at the point observed, bisected the angle between the
lines from it to the eye and the illuminating flame. The light
being thus polarized in a horizontal plane, was depolarized (that
is, compensated) by turning the glass plates through the neces-
sarv angle, the percentage corresponding to which was immedi-
ately found by means of the curve.
If we suppose a line drawn from the place of observation to a
point in the zodiacal light, and another drawn from the sun to
this at its nearest point, the two lines would meet at right
angles ; and a surface at the point of intersection must be so
placed as to have an incidence of 45^ in order to send the re-
flected light to the eye of the observer. We may in general
assume that there would be as many meteoroids on the nearer
side of the line from the sun as on the other. Those on the
more remote side, while presenting a larger illuminated surface,
would reflect the light at a smaller angle, and therefore polarize
a smaller amount of it. Those on the earthward side would
send less light to the earth, but polarize a larger proportion of
it. The differences would so nearly complement one another
that we may take their united effect as equivalent to that of a
body placed at the point of intersection mentioned above. For
this reason the objects tested were so placed that the angles of
incidence and reflection were 45°. .
Some of the substances, and the percentages obtained, were
as follows : — ^Porphyry, ground smooth but not polished, 35 per
cent. ; another surface thickly covered with accumulated dust,
16*5 ; dark blue shale, 25*7 ; syenite, coarsely crystalline and
rough, 16'4; gneiss, rather fine-grained, 8*8; granite, fine-
grained, 11*8; red jasper, rough broken surface, 23*5; sand-
stone 12*1 ; brick, rough fragment, 8*1 ; the same, smooth sur-
face, 11*3; red Wedgewood ware, unglazed, 14*2; indurated
clay, light brown, 11; mortar, whitewashed surface, 12*1; the
same, rough side^ 6 ; white chalk, cut plane, 2. A fragment of
the great meteorite of Pultusk, which the writer owes to the
kindness of Professor 0. C. Marsh, gave from a broken surface
11*7, from the blackened surface, 36 percent, of polarized light.
It is of the stony class, and of a light bluish grey colour.
The results show that from surfaces of this nature the light
reflected has in general but a low degree of polarization, not
Digitized by VjOOQ IC
On the Constant Currents in the Air and in the Sea. 21
greatly different, on an average, from that found in the zodiacal
light. Although no certain conclusions can be drawn from ex-
periments like these^ their results are not inconsistent with the
supposition in reference to which they were made, but, so far as
they go, tend to confirm it. The results of the investigation
may be summarized as follows : —
1. The zodiacal light is polarized in a plane passing through
the sun.
2. The amount of polarization is, with a high degree of pro-
bability, as much as 15 per cent, but can hardly be as much as
20 per cent.
8. The spectrum of the light is not perceptibly different from
that of sunlight, except in intensity.
4. The light is derived from the sun, and is reflected from
solid matter.
5. This solid matter consists of small bodies (meteoroids)
revolving about the sun in orbits crowded together toward the
ecliptic.
Yale CoUege, April 6, 1874.
IV. 7%^ Constant Currents in the Air and in the Sea : an At-
tempt to refer them to a common Cause. By Baron N. Schil-
ling, Captain in the Imperial Russian Navy*.
Introduction.
THE currents of the sea and of the atmosphere have been
observed from times immemorial ; much has been written
on both ; but, unfortunately, science has hitherto made but very
unsatisfactory progress in this department. The laws which
govern them are still very little understood ; and their origina-
ting causes, in particular those of the great ocean -currents and,
indeed, of the trade-winds, are as good as totally unexplored,
since, on closer examination, every explanation yet given must
be regarded as not at all sufficient. A complete knowledge and
u comprehensive theory of all currents will long remain impos-
sible, because the currents are subject to the action of very
various influences, and these, accompanied by very manifold cir-
cumstances, exhibit themselves in such different fashions and
are so complicated that it has not hitherto been possible to sub-
mit them to exact mathematical analysis. Apart from the theo-
retical difficulties, practice often opposes insuperable obstacles
when we wish to trace a current through the whole extent of its
* Tranilated from a separate publication commuiiicated by the author,
entitled Die bestandigen Strdmungen, &c., Berlin, 1874.
Digitized by VjOOQ IC
22 Baron N. Schilling on the Constant Currents
course* The air-currents escape our observations in the upper
strata of the atmosphere^ and those of the sea in the depths of the
ocean* Notwithstanding all the improvements of nautical instru-
meuts, we still possess no means of accurately determining the
currents at sea. Usually the ship's reckoning (f . e. the distance
run in a certain direction) is proved from time to time by astro-
nomical determinations of latitude and longitude ; and the dif-
ference thus brought to light is without hesitation attributed to
currents, although it may often result from quite different causes.
Although the unsatisfactoriness of this method has long been
acknowledged^ it is still universally retained for want of a
better.
The currents of the sea and those of the atmosphere have
hitherto been considered apart — ^probably because water and air
are^ in many respects, so very different ; but, in spite of this
great difference, there can be no doubt that the movements of
the sea and of the atmosphere, as fluids, are subject to the same
general laws. For, in air as well as in water, gravity is the
force which generates currents, because it tends to restore equi-
librium wherever it has been disturbed. But equilibrium is
disturbed only by the following three principal causes, which,
again, are the same for sea and air : —
A. Alteration of the specific gravity of the water or air ;
B. The rotation of the earth on its axis ;
C. The attraction of the sun and moon.
We see, then, that the currents of the sea and the air depend
on the same principal causes, and hence cannot well be separated
in the consideration of their theory ; only the following circum-
stances must be kept in view.
1. The air is a highly elastic, readily expanding, gaseous
body, while water is almost entirely destitute of elasticity.
2. The atmosphere is heated by the sun principally in the
lower strata, causing them to expand, become lighter, and, as-
cending, communicate their heat to the higher. The sea, on
the contrary, is heated by the sun's rays on its surface only to
a very slight depth, and, in consequence of evaporation, gives up
the greater part of its heat, as latent heat, to the air.
3. In the atmosphere we mostly observe only the currents of
the lower strata, and pay little attention to the upper currents,
though the latter are often very different, both in direction and
velocity, from the lower. In the water, on the other hand, we
direct our attention mostly to the upper currents; and only
quite recently have temperature-determinations at greater depths
begun to throw a scanty light on the deeper currents of the
ocean.
4. The seas are bounded by continents, which set impassable
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in the Air and in the Sea. 28
lifluts to the currents^ and thereby exert great influence on their
direction, extension, and velocity. It is quite otherwise with
the atmosphere, which encompasses the globe, and is undisturbed
in its free motion, save, perhaps, in some degree by lofty moun-
tain-ranges. But, on the other hand, currents may arise in the
atmosphere through the influence of the interior parts of the
continents, to which the sea has nothing to correspond.
Lastly, mention should be made of a certainly only conventional
difference between air- and ocean-currents. This is, that the
winds are universally named after the point from which they
come, while ocean-currents always bear the name of the point
toward which thev flow. This difference of nomenclature ap*
pears at first sight inconvenient; but use has so naturaliied
these designations in all languages that, as Laughton^ quite cor-
reetly remarks, any attempt to alter this custom would ouly give
rise to misunderstandings. To impress this upon young sailors,
the following phrase is used in the Russian navy : — *^ The wind
blows to the card ; currents flow from the card.''
The differences just mentioned between the air and water ex-
plain why the currents in the atmosphere often appear to us
quite different from those of the ocean, since the two classes of
currents are exposed to the action of so manv and various colla-
teral circumstances that the community of their fundamental
laws can almost be no longer discovered. And yet we must be
clear about these fundamental laws before we can enter upon the
consideration of the collateral actions.
The constancy with which the great ocean-currents and the
trade-winds move, and the analogy which prevails between them,
justify us in believing that they are less exposed to the opera-
tion of secondary causes and, therefore, are especially adapted
for the study of the general laws of currents. Hence we will
examine singly the above-named three causes, which, to our
knowledge, are alone capable of disturbing the equilibrium of
the sea and the atmosphere. We will ascertain how far each of
them is to be regarded as a generator of the constant sea-cur-
rents and the trade-winds, and in what measure it answers to
the existing explanations of these currents. The shifting winds
and smaller coast-currents we will in general leave unnoticed,
because (as already said) our information is still much too
limited for us to be able to form even the remotest idea of a
theory embracing all currents.
However, before we come to the examination of the forces
which call forth the constant currents, we will briefly describe
the great oceanic currents and the trade- winds, and indicate how
* Physical Geography (London, 1870), p. 176.
Digitized by VjOOQ IC
24 Baron N. Schilliug an the Constant Currents
the origination of these natural phenomena is at present ac-
counted for.
Constant Currents and Trade-winds, Views hitherto held on
their origin.
The analogy which subsists between the constant currents of
the different oceans, as well as between the trade-winds and the
equatorial currents, is most striking.
Both in the Atlantic and in the Pacific and Indian Oceans
there flows from east to west, on each side of the equator, a cur-
rent extending over about 20 degrees of latitude* and many
thousand feet deep. This is named the equatorial current^
while for more particular designations the names of the ocean
and hemisphere in question are added. Between these two
equatorial currents, there is found in all three oceans, nearly on
the equator, a relatively narrow zone, in which either no current
or one flowing in the opposite direction is observed. The equa-
torial streams continue their westward course till they encounter
coasts, which turn aside their direction, according to the posi-
tion of the coasts, and give them a more or less meridional direc-
tion, until, in both hemispheres, in the vicinity of 40^ lat. they
turn eastward to intersect the ocean again in this direction*
This latter stream, flowing from west to east, pretty well takes
in a zone of 10 degrees of latitude, and in all the oceans and
both hemispheres is met with between the 40th and 50th
parallels. This stream has different denominations in different
oceans ; but Miihry gives it the general name of the equatorial-
compensation stream ; for, arrived at the eastern boundary of
the ocean in question, the stream turns back again into the
equatorial region, to begin afresh its westward course. In this
way, in each hemisphere, regular circulations are formed, which
are comprehended under the denomination of rotation-currents.
In the centre of these circulations, about in the region of the
80th degree of latitude, there is in all the oceans a broad strip
in which no current is observed, and which is known by the
name of the Sargasso-sea. To these currents parallel to the
equator, with their included streamless zones, the trade-winds
with their zones of calms exactly correspond. On each side of
the equator there is a zone from 16 to 20 degrees broad in which
a constant trade- wind blows in the principal direction of east to
west. In the vicinity of the polar boundary of this zone the di-
rection of the wind is indeed mostly, in the northern hemisphere,
from the north-east — and in the southern, from the south-east.
In the middle latitudes, chiefly between the 40th and 50th
* In the Indian Ocean the northern equatorial current, interrupted by
the south coast of Asia, has less breadth.
Digitized by VjOOQ IC
in the Air and in the Sea. 25
parallels^ therefore entirely as with the compensation-currents,
constant west winds prevail, under the name of anti-trades.
Between these constant air-currents there are, just as with the
' sea-currents, both in the vicinity of the equator and not far from
the 80th degree of latitude in both hemispheres, zones of no
wind, which are known by the name of the equatorial and the
tropical calms. The trade-winds, with the calm-zones belonging
to them, shift a little with the seasons — ^in the summer of the
northern hemisphere moving somewhat northward, and in the
winter toward the south. In the currents of the ocean this
shifting of the zones is less marked; hence the currents of
water and air do not exactly correspond ; yet, excepting slight
deviations, the trade-winds with their calms present the same
picture as the equatorial currents with their streamless zones.
In spite, however, of this striking similarity, the trade- winds
have till now been ascribed to quite different causes from those
of the gre-at rotation-currents of the ocean.
We shall presently return to this subject; we will now only
mention further that the rest of the great currents in the dif-
ferent oceans likewise correspond so completely that the exist-
ence of very determinate laws must thence be inferred. Thus
the Gulf-stream and the Japanese Kurosiwo exhibit precisely
the same phenomena : both are currents of warm water, flow in
a north-easterly direction, and are separated from the coast to
the west of their course by a cold current flowing in the oppo-
site direction. The cold current of Peru corresponds to that of
South Guinea, just as does the warm Brazilian current to that
of Mozambique. Lastly, a feeble current from south-west to
north-east prevails in the entire south polar sea.
The trade- winds have from the 17th century been represented
as polar winds which are deflected from the direction of the meri-
dian by the earth^s rotation : this theory was, as far as we know,
first set up (very imperfectly, it is true) by Varenius, in 1660;
it was subsequently improved by Halley in 1686, and Hadley
in 1785, and is for the most part named after the latter, as it
has since made no advance. That this theory has been so gene-
rally accepted is so much the more surprising, as many pheno-
mena of the trade-winds are scarcely in accordance witn it.
According to this theory, the masses of air in the equatorial
regions, rendered lighter by heating, are continually ascending,
through which the cooler and heavier air of higher latitudes is
impelled to flow toward the equator. As the velocity of rota-
tion is greater at the equator than at any other latitude, and
gradually diminishes to the poles, while the air-particles (by the
law of inertia) do not at once take up this greater velocity as
soon as they arrive at parallel circles where the motion is more
Digitized by VjOOQ IC
26 Baron N. Schilling im the Constant Currents
rapid, the polar wind is turned westward, and expresses itself in
the northern hemisphere by a north-east, in the southern by a
south-east wind. In the higher strata the ascending air returns
to the poles to serve as a compensation for the air which has
flowed thence to warmer latitudes. As this upper anti-trade
streams polewards, it receives from the rotation of the earth a
deflection eastward in both hemispheres. Compressed by cool-
ing and the polar convergence of the meridians, it sinks at about
the latitude of 80^ to the surface of the earth and so forms the
constant west wind of the middle latitudes. The ascent of the
air at the equator and its descent in 30° lat. will produce in the
first case the equatorial calms, and in the second the calms of
the tropical zones.
This is, as briefly as possible, the generally recognised theory
of the trade-winds, which, however, is not at all adapted for ex-
plaining the perfectly analogous rotation-currents of the ocean.
The equatorial current is still regarded by manv as a drift-
stream produced by the trade-winds. This already long-per-
sistent opinion received such a confirmation by the authority of
Franklin and Rennell, that, notwithstanding its forcible refuta-
tion by Maury and MUhry, it is still maintained, although only
in England. For instance, Herschel, Carpenter, and Laugh-
ton have recently pronounced in favour of this explanation.
Far more prevalent, however, is now the view that the cause
of the equatorial current is to be sought immediately in the
axial rotation of the globe. Columbus, the discoverer of this
current (in 1492), accounted for it by the universal motion of
the heavens {con los ciehs) from east to west*. This notion of
the ^'primum mobile ^' was followed by all, till Kepler at the
commencement of the 17th century pointed out, and Yarenius
(1650) proved in detail, that the current was occasioned not by
the "primum mobile/' but by the rotating motion of the earth,
the water not being able to keep up with the earth^s rapid mo-
tion. Miihry, the chief authority on ocean-currents, substanti-
ally shares this view, only giving to it a different and not quite
intelligible expression. He saysf* as Fourier j: before him, that
the staying behind of the water is effected by the centrifugal
force of the earth. By this expression we are accustomed to
understand the force that throws off from the centre, which
always acts in the direction of the radius of each parallel circle ;
and hence we cannot see how this force could cause the swift-
ness of rotation of the water to be less than the rotation-velocity
of the entire globe.
♦ Kohl, Geschichte des OolfstromSt p. 30.
t Ueber die Lehre von den MeereS'Stromungeny p. 5.
J Ann. de Chim, et de Fky$. 1824, p. 140.
Digitized by VjOOQ IC
m the Air and in the Sea. 27
On the other hand^ Miihry accounts for the compensation-
corrent, flowing in the middle latitudes from west to east, by
the aspirating or attracting force of the equatorial current — that
is, by the tendency of water to find its levels which impels it to
fill up the void caused by the primary current. He therefore
makes the aspirating force operate in a vast arc across the
entire ocean^ and chiefly between the 40th and 50th parallels of
latitude — a decided circubu vitiogus.
The meridional currents* are mostly accounted for by the
constant difference of temperature of the equatorial and polar
re^ons ; and Miihry attributes to the cold and heavy polar flow
the primary, and to the warmer and lighter compensating anti-
polar flow the secondary action. At the same time, in conse-
quence of the velocity of the earth^s rotation progressively dimi-
nishing in the direction of the poles, all the cold or polar streams
receive a deflection of their direction to the west, and the warm
autipolar currents a deflection eastward. Franklin and Bennell
explained also the meridional currents by the action of the
trade-winds ; for they believed that by the driving force of these
winds the waters are accumulated in the Gulf of Mexico and
are discharged in the Gulf-stream, — a view that probably now
possesses scarcely any adherents.
Having briefly indicated the existing explanations of the
origin of the great ocean-currents and the trade-winds, we will
now endeavour to ascertain in what manner each of the three
forces before mentioned is capable of acting upon the currents,
how their influence must express itself, and, finally, how far the
explanations hitherto given correspond with the facts.
A. Alteration of the Specific Gravity of the Water
AND Air.
a. Difference of Temperature.
Every material substance possesses the property of occupying
a greater space when its temperature is raised, while still re-
taining the given number of its molecules and its weight. From
this it follows that, after a rise of temperature of a body^ fewer
of its particles can find room in a given space; so that the
specific gravity must diminish with rise of temperature. Sub-
stances of different kinds differ widely in their degrees of ex-
pansion, and hence also in the alteration of their specific gravity.
According to determinations by Ermanf, sea- water expands
0*00027 of its volume with every degree between 0** and 12° R.
On this ground it has been calculated ;[ that the entire mass of
^ These, which flow in the direction of the meridian, Miihry calls lati-
tudinal. T Pogg. Ann, vol. xz. p. 114.
I Biflchof, Lehrbuch der chem, u, phys. Oeologie, p. 7-
Digitized by VjOOQ IC
28 Baron N. Schilling on the Constant Currents
equatorial water would stand 14 feet higher than the water of
the polar seas^ if it could not flow off. It has been thought
that this tendency of the equatorial water- surface to rise would
serve to account for the Gulf-stream^ which accordingly would
flow down hill. But this inconsiderable elevation of the surface
of the equatorial sea would not give a fall of even ^ inch in a
German mile, which, in relation to the velocity, is much too
little. Even the assumed elevation of the surface, however, can
never actually be produced; for as soon as any particles of
water become a little lighter, they must, in obedience to the law
of gravitation, immediately spread uniformly over the entire
surface. Thereby is necessarily produced a flow of the warmer
and therefore lighter superficial water to the colder regions, and
of the heavier cold water at the bottom to the warmer regions.
Such an exchange of the waters of the warmer and colder seas
exists in reality. A proof of this is furnished by the tempe-
ratures of the ocean diminishing with increasing depth — the
temperatures of the greater depths being very low, even in the
equatorial regions. An exception to this rule is formed by
those seas which are divided from the ocean by a ridge over
which the water is considerably less deep. In such seas the
temperature sinks merely to a depth corresponding to the height
of the water above the ridge, and below that remains nearly
unaltered, because the colder water, cut off by the ridge, can
have no influx. We have an example in the Mediterranean,
united with the ocean by the Straits of Gibraltar, the depth of
which is onlv a little over 100 fathoms, — and in the Skagerrack
and some Norwegian fjords, for which the bottom of the pro-
portionally much shallower North Sea forms a ridge. It is
therefore unquestionable that water flows at the surface of the
sea out of warmer into colder, and in its depths out of colder
into warmer regions ; so that there only remains to get an idea
of the velocity of these currents.
Water, as a bad conductor of heat, is warmed only very
slowly, and expands just as slowly. Now, as this expansion is
moreover very trifling, the streaming produced by difference of
temperature must likewise be only an extremely slow, creeping
motion.
In order to give an idea of the origination of the meridional
currents from difference of temperature. Dr. Carpenter showed,
on the 9th January 1871, at the Royal Geographical Society in
London, the following experiment. He filled a glass tank,
several feet long, with water, which at one end of the tank he
cooled with ice, and at the other end, bymeans of a special
arrangement, he heated at the surface. The cooled water was
coloured red ; the heated, blue. At the close of the lecture.
Digitized by VjOOQ IC
in the Air and in the Sea. 29
which may have lasted an hour^ the blue water had moved along
the surface^ and the red along the bottom ; but^ notwithstanding
the pretty considerable difference of temperature and the length
of time, the coloured water particles had travelled only a few
feet. This experiment proves, therefore, only what we have
already said — ^that through difference of temperature an ex-
change of the water particles must take place, but that this
exchange proceeds verv slowly, even with considerable difference
of temperature and with little distance between the differently
heated waters.
In nature, however, the difference of temperature of sea-
water is proportionally inconsiderable, never amounting in the
whole to more than about 80^ C, while this difference is dis-
tributed over the vast distance of the polar from the equatorial
seas. It thus appears, then, impossible that this cause can have
power to set in motion such a current as the Oulf-stream. Even
the mass of the heated water, which is so readily invoked, cannot
here exert any accelerating action, because only an incon-
siderable superficial layer is warmed by the sun, and nothing
hinders the direct, gradual, and immediately complete inter-
change of the water particles. Only when large basins of
water of different temperatures are united by a channel can the
mass of the warmer water play a part, and the difference of
temperature generate a considerable current in the channel.
Thus, for example, we may regard the northern part of the
Atlantic between Norway and Greenland as a broad channel
connecting the north-polar basin with the ocean.
The air, however, expands 15 times as much by heating as
water^ and the influence of temperature-difference on air-
currents is undeniable ; yet even here that influence is generally
very much overrated. For air, as well as water, is a bad conductor
of heat, and therefore only slowly changes its temperature and
therewith its specific gravity. Hence we are decidedly of
opinion that the expansion of air by heating in the open can at
most occasion only a gradual inflow of air^ never a sudden gust
or a rapid fall of the barometer. The gradually heated air
rises only gradually and slowly, and is just as slowly replaced
by cooler air. A burning light, or a cbimney-fire gives us the
best proof of the correctness of this assertion. Although the
temperature produced in the fireplace is incomparably higher
than ever occurs in nature through the heat of the sun, and the
draught is artificially increased by the height and narrowness
of the flue, yet this draught is so inconsiderable that it can
seldom carry up a piece of paper thrown into the chimney, and
even the ashes of burnt paper are hardly lifted. This shows us
that even a strong heating occasions only a slow ascent of the
Digitized by VjOOQ IC
80 Baron N. Schilling on the Constant Currents
air ; so that by it^ at all events in ordinary circumstances, a
breath of air, but no wind, can be produced. In a forest-con-
flagration, the enormous heat appears to cause a considerable
ascending current of air; but even then the inflow of air
thereby e£fected is perceptible only in the immediate vicinity of
the burning.
Hence we believe that wind can mostly arise only from con-
densation of the aqueous vapours in the atmosphere, which
possess the property of very suddenly changing considerably
their degree of elasticity and the pressure resulting from it ;
this must, of course, exert a great influence on all atmospheric
phenomena. Certainly the elasticity of the aqueous vapour
stands in the closest relation with the temperature, which so
far, therefore, operates indirectly in the origination of wind.
Whether change of temperature is the only cause of the con-
densation of vapour, we know not : as, when the aqueous vapours
are condensed, electricity is always set free, perhaps conversely
the condensation may be caused by electricity.
At any rate it is changes in the tension of the aqueous vapour
that produce strong winds ; and only in very peculiar cases can
the, by itself, slow expansion of the air develop stronger winds.
Thus, for instance, when the greater portion of a continent is
powerfully heated by the sun, the mass of air rising, though
only slowly, from the whole of the vast surface, would require
for its replacement (that is, for the restoration of equilibrium)
such a mass of air that the inflow must be much accelerated,
because it forms a stratum of little height in comparison with
the magnitude of the heated surface. An example of winds
thus produced is afforded by the monsoons. Over the ocean the
atmosphere can never be so much heated as over the land ; and,
besides, evaporation of the water of the sea and the elasticity of
the aqueous vapour are augmented as the temperature of the air
rises. If, therefore, the expansion of the air diminishes the
atmospheric pressure, on the other hand the augmented elasticity
and quantity of aqueous vapour will again increase it ; and it is
difScult to decide which of these two may exert the greater in-
fluence. Admitting that the diminution of the atmospheric
pressure by expansion of the air is greater than the rise of the
pressure by aqueous vapour^ it yet appears to us self-evident
that the wind resulting from the heating of a continent must be
much stronger than that produced by the heating of the air
over the ocean, supposing both to take place over very consider-
able spaces.
If, then, the recognized theory of the trade-winds were cor-
rect and they were produced by the ascent of the heated air, the
trade- winds would blow in summer towards the Sahara, since
Digitized by VjOOQ IC
in the Air and in the Sea. 81
there the thermometer not seldom shows 50^ C. in the shade^
while in the equatorial regions of the ocean the temperature of
the air never rises above 30** C. The trade-wind, however, at
the north-west coast of Africa blows constantly from the desert,
carrying the fine sand far out to sea.
Farther, in summer the temperature of the 20th and 30th
degrees of latitude is not lower, indeed it is higher than that of
the equator, and yet the shifting of the trade-zones is inconsi-
derable, and the wind keeps its usual direction.
Likewise, according to Hadley's theory an ascending or a de-
scending current should prevail in the calm-zones. Now this
current must be very considerable, if it brings forth the fresh-
blowing trades and anti-trades ; and the ascent of the air in the
equatorial calms, and its descent in the tropical calms, would
make themselves perceptible, even if the motion were very slow.
This, however, is not the case : a particle of dust loosened from
the sails falls, both in the equatorial and the tropical calm-zone,
quietly to the deck, without exhibiting the slightest tendency to
be impelled upward or downward. From this we conclude that
the upward and downward currents of air in the zones of calms,
if they really exist, must be so slight that the generation of the
trade-winds and anti-trades cannot possibly be ascribed to
them.
Let it further be remembered that in the middle latitudes of
the northern hemisphere the anti-trade often blows from the
north-west instead of south-west, and in the southern hemisphere
from south-west instead of north-west — which could not be, if,
as required by Hadley^s theory, it formed a current directed
toward the poles.
Lastly, in Central Europe these constant west winds blow in
summer very moderately, while in winter their force is much in-
creased— which again does not correspond with the theory ; for
in summer the eastern steppes are strongly heated and should
attract the west wind, while the cold which prevails in Eastern
Europe in winter would, on the contrary, contribute to the
weakening of the west wind.
All this and many other reasons'^ show that the existing
theory of the trade-winds is not sufficient to account for the
phenomenon, and that another must be sought.
We do not on this account dispute that heated air must
ascend ; we only believe that, since the heating and expansion
proceed very gradually, the ascent must also be very slow and
hence cannot constitute the principal cause of the trade-winds.
Their main motive cause appears therefore to lie in other forces,
of which we will speak subsequently.
* Laughton, 'Phyrical Geography,' pp. 120-127.
Digitized by VjOOQ IC
82 Baron N. Schilling on the Constant Currents
If, then^ difference of temperature can only call forth incon-
siderable winds by the expansion of the air, it is clear that in
water, so much less expansible, heated to only a proportionally
slight depth, no great current can be generated by this cause.
If this force were sufficient to occasion a considerable current, it
would extend over the entire surface of the ocean, and not merely
show itself in a narrow strip at its margin.
We nevertheless allow that the heating of the water may, in
certain cases, have an important influence on the maintenance
and extension of an already existing current. If, e. g., a cur-
rent arising from other causes strikes upon a coast, it usually
takes the direction of this coast, along which it continues until
it gets beyond the sphere of the action to which it owes its de-
velopment. But if it accumulates at the coast the heated sur-
face-water of the sea, the mass of warmer and lighter water,
continually replaced, will perpetually exhibit the endeavour to
spread over the heavier water of colder regions. Difference of
temperature will therefore in this case have an essential influence
on the continuance and the direction of the currents toward
higher latitudes, but cannot independently generate the currents.
This, then, explains to us also how it is that warm and cold cur-
rents are found preeminently at sea-coasts. The first impulse,
however, to the flowing which collects the heated water does not
arise from difference of temperature, but always from other
causes. The ascertaining of these initiating causes is of very
great importance for the foundation of a theory ; for without
accurate knowledge of the fundamental laws, we can get no
account of the action of the accessory causes.
Let us now consider the possible influence of evaporation. As
already said, the evaporation of water is in close connexion with
heat ; for with a rise of temperature the capability of the air to
take up aqueous vapour is also increased. Hence much more
water is evaporated in the equatorial regions than in higher
latitudes; and the vapours are driven by air-currents into other,
cooler regions, where, on the cooling of the air, they are given
back to the sea as an atmospheric precipitate. Evidently from
this cause must arise a sea-current toward the equator, though
only a very inconsiderable one. Miihry calculates that in the
tropics about 15 feet of water evaporate yearly, therefore
about half an inch daily. Perhaps half of this evaporation is
returned to the tropical seas as rain and river-water, and only
the other half (J inch daily) returns by sea-currents from higher
latitudes. But a current which in the course of 24 hours re-
places only a layer of water a quarter of an inch in thickness,
must be imperceptible. This slight current flows at the surface,
and is directed to the equator ; it thus counteracts the current
Digitized by VjOOQ IC
m tlie Air and in the Sea, ' . 83
arising from difference of temperature, which, as above remarked,
must flow at the surface from warmer into colder zones.
Evaporation, then, also cannot occasion any perceptible cur-
rent in the open sea ; but in channels connecting an inland sea
with the ocean a diflerence of level between the two seas, arising
from greater evaporation of the inland sea, may occasion a strong
current. We have instances of this in the Straits of Gibraltar
and Babelmandeb.
Let us now turn to the consideration of the influence which
heat may have indirectly on the origination of sea-currents
when, through its action upon the aqueous vapour in the atmo-
sphere^ it generates wind. The action of wind upon the surface
of water is familiar not only to the inhabitants of coasts, but to
almost every one. Indeed we see in every pond how the water
is driven by a strong wind ; and if the basin is flat and not very
deep, not seldom does the water recede from the windward
side, and accumulate on the lee side. Such heapingsup of the
water in shallow bays, and at the mouths of great rivers, by
strong winds occasion inundations. At a straight coast-line,
too, the water may rise considerably by the force of the wind,
if the depth inci*eaBe8 very gradually and thereby the outflow
beneath is checked.
Indeed, on the open sea the wind often drives the water
before it, and thereby forms what ai« called drift or superficial
currents ; but these, as irregular phenomena, do not here come
into consideration; we can only occupy ourselves with those
currents which are called forth by constant winds, t. e, the
trade-winds. Even the constant action of the trade-winds,
however, is hardly able to occasion any very deep-going current,
as has already been sufficiently shown by Maury and Muhry.
According to FitzRoy^s data, the highest waves rise to the
height of 60 feet*, measured from the trough to the crest of the
wave, therefore 30 feet above the smooth surface of the sea. If
we might assume that the entire wave could be driven forward
by the wind (which is decidedly assuming too much), thus
would be produced a current of 30 feet depth. Through the
friction of the water-particles, the efiect of the wind upon the
current may become sensible somewhat deeper still ; but the
* This number appears to us very high ; for we have often, in a severe
storm, ascending the shrouds, tried to bring our eye into such a position
that, at the moment when the ship was exactly in the trough, we could
see several wave-crests in a hori2ontal Hne. The height of the eye above
the ship's water-line then determines the greatest height of the wave. In
this way J have only once at Cape Horn (where the waves rise uncommonly
high) measured a height of 46 feet, and at the coast of Japan, in a typhoon,
one of 38-40 feet ; at other times the height was mostly less than this.
P/uL Mag, S. 4. Vol. 48. No. 315. July 1874. D
Digitized by VjOOQ IC
34 Baron N. Schilling; on the Constant Currents
b
flowing must rapidly diminish downward^ and soon entirely
cease. A. Findlay* thinks that the wind can never call forth
a current of greater depth than 5 fathoms. James Croll's re-
mark t> that the duration of the wind, as well as its force, must
have great influence on the depth to which it acts, may to a
certain extent be quite correct ; but, nevertheless, action of the
wind upon currents at a depth of thousands of feet (as, for in-
stance, in the equatorial current) is not possible; hence we
must see that Franklin and Rennell's view, that the equatorial
current results from the action of the trade-winds, cannot be
true.
Nature herself gives us decisive proofs against that view.
With the shifting of the zone of calms it happens that the
equatorial current flows just as well in that zone as in the trade-
wind. In the Indian Ocean the change of the monsoons has
scarcely any influence on the equatorial stream. The Gulf-
stream often flows in opposition to very violent storms, which
would be impossible if its motive force lay in the trade-wind.
Even the opinion that the trade-wind raises the level of the
Gulf of Mexico, and so produces the Gulf-stream, is untenable.
In the flrst place, it is proved by the levelling of the isthmus of
Panama and the peninsula of Florida that this is not the case,
as the level of the Mexican Gulf pretty closely accords with
both that of the great ocean and that of the Atlantic. Secondly,
in the open sea an enduring higher level can never be product
by the action of the wind ; for as soon as any particles of water,
driven by the wind, change their place, they compel by their
pressure just as many others immediately to take the place lef^
free by them. Only where the formation of the coast hinders,
or at least impedes, this back-flowing motion, can an alteration
of level take place.
Certainly the mechanical pressure of the wind upon the sur-
face of the water can, in the open sea, somewhat alter the level ;
but as the wind mostly acts horizontally, or at a very acute
angle, upon the surface, the mechanical pressure is so little
that the oscillations of the sea-level brought about by it must
likewise be inconsiderable.
Just so must the variations of the atmospheric pressure exert
an influence on the height of the water of the seas, and con-
sequently also on their currents. When, for example, the
barometer falls an inch, the surface of the sea at the place must
rise 13'6 inches, and vice versd, and thus a current be formed
from where the pressure is high to the region where lower pres-
♦ A Dictionary for Navigation of the Pacific Ocean (London, 1851),
vol. ii. p. 1222. Also Miibry, Geograph. Mittheilungen, 1872, p. 136.
t Phil. Mag. October 1871, p. 2G8.
Digitized by VjOOQ IC
in the Air and in the Sea. B5
sure prevails. It is self-evident that a current thus produced
in the ocean can only be very inconsiderable and inconstant,
since it changes with every change of the atmospheric pressure.
This foi-ce, again, can only make itself perceptible in channels.
Suppose that on an inland sea connected with the ocean
only by a strait the barometer suddenly fell 1 inch, the level of
this sea would stand 13*6 inches lower than equilibrium with
the ocean at the moment would require. The mass of water
wanting must therefore pass from the ocean through the strait.
We must ascribe it to this circumstance that, in the Sound, a
change in the direction of the current mostly occurs 24 hours
before a change in the direction of the wind. Just so the water
usually rises in the Gulf of Finland before the south-west wind
comm^ices; and this rise is noticed also in winter, when the
entire surface of the sea is covered with ice, and thereby the
direct action of the wind is withdrawn.
b. Saltness of Sea-water.
Alterations in the saltness of seas greatly aflfect the specific
gravity of the water. The observations, however, which have
been made in different parts of the world have proved that the
difference in saltness of the various oceans is extremely slight 'i^.
This compels as to the conclusion that currents immediately
tend to equalize the slightest difference in the saltness of the
water.
The causes of change in the saltness may be accidental and
temporary, or constantly repeating themselves in certain regions.
In the first case they produce variable currents, which do not
belong to the subject we are considering; but in the second
they must confer upon the water a constant tendency to inter-
change, and call forth constant currents.
In the equatorial regions^ for example, the half inch of water
evaporated daily leaves constantly its salt behind, which, with
the vast depth of the ocean, can hardly add perceptibly to the
specific gravity of the rest of the water.
Nevertheless this water, very gradually becoming slightly
Salter and heavier, and sinking, must occasion in the depths a
current, although a very feeble one, the direction of which must
be into the regions where there is little evaporation and consider-
able atmospheric precipitation, therefore into higher latitudes.
Consequently, as we have already seen, the current called forth
by the evaporation of the water counteracts that which is pro-
duced by the expansion of the water from difference of tem-
perature.
* ** On the Composition of Sea-water in different parts of the Ocean,"
Pbil. Trans. Roy. Sck?. London, 1865. ]). 203.
D2
Digitized by VjOOQ IC
86 Baron N. Schilling on the Constant Currents
In the polar sea much water is, in winter, turned into ice,
and its salt separated. This salt adds, though only inconsider-
ably, to the specific gravity of the cold, and hence already heavy,
polar water, and^ebntributes a little to the undercurrent in the
dii*ection of the equator ; so that it acts, contrary to the pre-
ceding case, just the same as the difference of temperature.
Perhaps it is partly owing to this, that the flow of the Gulf-
stream is somewhat stronger in winter than in summer.
In an extremely interesting article on the currents at the
southern extremity of America, Miihry*, on the ground of the
winter temperature of Patagonia, conjectures that the Brazilian
current also is stronger in the winter of the southern hemi-
sphere than in summer.
In summer, when the polar ice melts, a superficial polar
current results; for the water from the melting of the ice,
having but little saltness, remains at the surface in spite of its
coldness. Scoresby remarked that near Spitzbergen the water
of the surface was warmer than at some feet depth ; and this
observation has been recently confirmed by the Swedish Expe-
dition and by the Norwegian Captain Ulvef*
Unfortunately, we do not yet possess any accurate determina-
tions of the greatest density of sea-water at different tempera-
tures and under various pressures. At all events, however,
Miihry^s view, that sea-water, as well as fresh water, attains its
greatest density at -h4^C., appears destitute of proof; for it
has recently been found that the temperature at very great
depths is often below 0^ C. It is probable that the great pres-
sure to which the water is there exposed has an influence in
preventing it from freezing, even below 0^ C. If earlier obser-
vations seem to contradict this, the reason may well be that the
thermometers were not sufficiently protected against the pres-
sure of the depths, and hence always gave the temperature of
the bottom too high. On this defect rests also Uoss's well-
known theory of a constant temperature of -h39^ F. at the
bottom of the sea.
At the mouths of rivers, the fresh water must spread upon
the surface, and therefore give rise to a current running out-
wards from the mouth, until it is mixed sufficiently with the
salt water. To this end, however, the heavy salt water will
flow in the opposite direction, toward the mouth — which, even
with a slight current, must greatly favour the formation of
sandbanks there.
In the case of inland seas where the inflow is greater than the
evaporation, as ^.^. in the Black Sea and the Baltic, just as
* Petermann's Geographische Miltheilungen, 1872^ vol. xviii. p. 12G.
Digitized by VjOOQ IC
in the Air and in the Sea. 87
"With rirer-mouths, the upper current in the channel of discharge
will flow outwards, while an undercurrent of constantly salt
water must flow inwards. But in seas where the evaporation
exceeds the influx (for example, in the Mediterranean and the
Red Sea), the upper current must flow in through the channel,
and the undercurrent carry out the superfluous salt. An
extremely interesting example of this sort is presented by the
Gulf of Karabughaz, which is connected with the Caspian b^ a
very flat channel of only a few feet depth. As the evaporation
from the very spacious surface of the gulf, into which no streams
flow, is very great, especially in summer, water is perpetually
flowing in from the Caspian with a velocity that sometimes rises
to 6 knots an hour. Of course this current brings much salt
into the gulf, from which it cannot get out again, because the
channel is too shallow to permit an outflow beneath. The salt
thus accumulating is deposited in crystals on the bottom; and
thus the Gulf of Karabughaz plays the part of a saltpan conti-
nually withdrawing salt from the Caspian Sea. If in the course
of time the sand washed in by the waves should completely
block up the shallow strait which joins the gulf to the sea (which
would long since have happened if the current were not so
strong), Karabughaz as a lake would soon evaporate completely
and leave behind a basin of solid salt, such as we see in the
Elton-See and in lletzkaja Saschtschita as formations of pri-
meval times.
If in any part of the ocean animal life be developed in greater
abundance than in others, the excessive abstraction of salt or
lime from the water by the animals will also give rise to slight
movements of the water. Although such movements could
scarcely be called a current, it cannot be doubted that such must
take place in the deepest seas even at the bottom, because other-
wise no life would be possible there ; for among the animals
living in the depths there are creatures that cannot change their
place ; nourishment must consequently be brought to them by
currents.
The theory of perfect stillness in the bottom waters of the
sea * is therefore, like the theories of Boss and Forbes, to be
regarded as incorrect.
We have thus examined all the causes which afiect the specific
gravity of sea-water and the air, and come to the conclusion thit
differences of temperature and in the saltness of the water of the
sea assist only in a slight degree in maintaining the great ocean-
currents and the trade-winds, but cannot possibly produce them ;
* Miifiry says, " At the bottom of the ocean we must assume that there
is almost complete stillness."— L^Are uber die Metres- Stromungen, p. 6.
Digitized by VjOOQ IC
38 Mr. R, Mallet on the Tidal Retardation
to explain the origiDation of these currents we must search for
other forces.
In certain cases, if an already existing current accumulates
the heated water in greater quautity, the diflFerence of tempera-
ture may indeed accelerate this current ; and in the air, if it
operates over very considerable spaces, it can generate wind ;
but in general it is the quickly condensing aqueous vapour
which, by the diminution of its tension, plays the chief part in
the production of wind.
[To be continued.]
V. Tidal Retardation of the Earth's Rotation.
By Robert Mallet, F,R,S.*
THE general idea of the retardation of the earth's rotation by
the great tide-wave acting as a friction-brake as it pro-
gresses under the coercion of the moon, commonly ascribed
to Mayer, was, I have good reason to believe, anticipated by
Emanuel Kant, though I have not been able myself to verify the
passage in his writings. Of the real existence of such a re-
tarding force, however small may be its effect, there can be little
doubt since the masterly researches of Adams upon the moon's
acceleration. The subject, probably from its inherent complexity,
has attracted but little attention, except from astronomical
mathematicians ; and some points respecting it which have been
referred to in more popular work8, appear involved in some ob-
scurity. Professor Tyndall, who, in his 'Heat a Mode of Motion,'
gives a very lucid popular account of the phenomena (almost,
as he states, in the words of Mayer), has in paragraph 697>
p. 483 (4th edit.), the following passage : — " Supposing, then,
that we turn a mill by the action of the tide, and produce heat
by the friction of the millstones ; that heat has an origin totally
different from the heat produced by another pair of millstones
which are turned by a mountain-stream. The former is pro-
duced at the expense of the earth's rotation, the latter at the
expense of the sun's heat which lifted the mill-stream to its
source." This distinction, it seems to me, cannot be main-
tained. The power of a tide-mill is not derived from the
rotation of the earth, nor from the retardation of that rotation
by the great tide-wave. The sea, no matter from what cause,
rises above its normal level, to which it after a time sinks again.
If during the interval we can impound a portion of the mass of
water so elevated and let it descend through some machine
recipient of water-power, we have the tide-mill, the power of
* Communicated by the Author.
Digitized by VjOOQ IC
of the Earth's Rotation. 89
which is as directly derived from gravitation as is that of a
water-mill upon a mountaia-streara. The water is raised in the
former case by gravitation towai*ds the moon and by gravitation
falls back towards the earth ; iu the latter it is raised by evapo-
ration^ and falls back to the sea by gravitation. It is true that
the earth^s and the moon's rotation are '^ inseparable accidents ''
to the rise and then the fall of the surface of the sea at any
particular point; but the source of the power is derived, not
from the mechanism nor at the expense "of the earth's rotation/'
but as directly from gravitation as is the case in any ordinary
mill-stream. If I am wrong in this I shall gladly accept cor-
rection. My chief object here, however, is to ask whether
(assuming the actuality of retardation of rotation by the tidal
wave acting as a brake, and be its amount more or less) there
may not be other forces in action upon our globe tending to
countervail this to a greater or less extent. It seems to me that
there arc — though, so far as my reading goes, I have not seen
-any notice of such on the part of physical writers. Every particle
of matter (rotating as part of our earth) which descends from a
higher to a lower elevation, must in doing so part with kinetic
energy proportionate to its decrease in velocity of rotation between
its higher and its lower positions, and the energy so lost is trans-
ferred at the lower point to the earth itself. Every drop of water,
therefore, every flake of snow that precipitates upon the higher
parts of our globe, if assumed to reach these points without
relative velocity, must in descending to the sea-level tend to
accelerate the earth's rotation. So also every block of ice or of
stone that descends from the mountain-tops, every particle of
detritus carried along from higher levels towards the sea, must
have the same effect. With regard to the first it may be said,
every particle of water raised by evaporation from the surface of
the ocean ascends into the atmosphere with only a velocity of
eastward rotation due to the earth's radius at the sea-level, and
at the latitude at which it is taken up, and that therefore when
precipitated upon some much higher level it takes away from
the earth as much kinetic energy as it returns to it in descending
in streams again to the sea-level. But is this so? What
actually passes when a particle of sea-water at the surface of
the ocean, parting with its salt, rises therefrom under the in-
fluence of the sun's heat, and becomes an invisible vapour
held in suspension by the air, is to a great extent still un-
known. The particle of water, whatever be its physical con-
dition on leaving the liquid surface, undoubtedly only possesses
the velocity due to its low position upon the earth's surface ;
before it has risen even a fraction of an inch, however, it is taken
possession of by the air (that is to say, by the winds) ; and all its
Digitized by VjOOQ IC
40 On the Tidal Retardation of the Earth's Rotation.
subsequent movemeDts are coerced by them. Except througa
the winds it has no point d^appui upon the solid earth. Now
the movements of the winds, however largely modified by the
form and rotation of our earth, mainly depend upon differences
of temperature produced by the sun's heat ; it would seem there-
fore that, so far as the kinetic energy of the ascending particle
of vapour is concerned, it may or may not affect, and, if at
all, very slightly, the horizontal motions of the winds, but can
have no effect upon the rotation of the earth.
The case is different, however, as soon as the particle of vapour
raised by molecular forces to the level of a mountain-top is pre-
cipitated thereon as rain or snow, and begins to desceod again
towards the ocean whence it came : at every foot of its descent
it parts with kinetic energy, which it transfers directly to the
earth as a whole. On the other hand, such particles of vapour
as assumed the form of rain or snow at greater or less elevations,
and fall directly as rain^drops to the sea-level, can produce no
effect in accelerating the earth's rotation, each drop being co-
erced in its movements until within a short distance of the earth
by the winds — that is, by the same molecular forces which raised
them up.
If this speculation be admissible, then we have a source of
sensible acceleration to the earth's rotation in the vast volume of
water which is precipitated upon the dry land and runs off into
the ocean. Adopting Gardner's estimate of the surface of the
land, exclusive of the antarctic continent, and assuming a mean
annual rainfall for the whole earth of 60 inches per annum, and
that two thirds of the entire rainfall returns to the ocean by
streams and rivers, we have 23,891 cubic miles of water annually
precipitated and fiEJling back into the ocean ; and assuming the
mean height of the land to be about 1000 feet, this immense mass,
on reaching the ocean, has lost kinetic energy due to the difference
in velocity of rotation between the earth's mean radius at the
sea-level and the same plus 1000 feet, the portion of this which
is effective in producing acceleration depending upon the cosine
of the latitude.
As respects the descent of solids from higher to lower levels^
there seems no room for doubt as to their tendency to produce
acceleration in the earth's rotation. It is true that at remote
epochs, when continents and mountains were originally ele-
vated, their uplifting tended to retard the earth's rotation, and
that their complete ablation could do no more than restore the
energy of rotation the earth had before their upheaval. But
the ocean- bed was depressed ; and its area is four times that of
the land, and its mean depth probably greater than the mean
height of the continents ; if, therefore, we assume the present
Digitized by VjOOQ IC
On some points in Mallet's Theory of Vulcanicity. 41
ocean-level as a datum plane^ the changes of level originating
land and sea may have tended rather to accelerate than retard
the earth's rotation. Taking the mean of the sediment stated
to be carried by six great rivers, namely the Mississippi, Po,
Vistula, Rhine, Ganges, and Rhone, it amounts to about y^Vir
in volume of the water discharged ; and if we apply this to the
water discharged from the whole surface of the land, as above
stated, we have -8j^^^= 19*90 cubic miles of sediment annually
discharged at the sea-level. These rough estimates are pro-
bably far from correct, and we do not know with any pre-
cision what is the mean specific gravity of this sediment, nor
from what mean height it may be considered to have descended ;
but we can easily see that the loss of rotative energy during the
descent of this vast mass, if transferred to the globe as a whole,
is scarcely negligible. Nor does this represent all that we have
to deal with. The sediment finally carried into the sea repre-
sents the real annual degradation of the land by rain and rivers ;
and the huge block that falls to-day from a Sierra summit and
wedges itself a few miles off immovably in the cleft of a canon,
though it may not reach the sea for thousands of years, daring
which it is slowly transformed into sediment, is nevertheless
effective, as is the ice which thaws or falls in avsJanche, in trans-
ferring to our earth the energy of rotation they lose in descent.
Whether or not it be true that, viewed on its largest scale and
at some indefinitely remote period yet to come, the movements
of all the bodies of the universe tend to ultimate rest, and an
end of the present order of things, it seems a fact that all the
smaller perturbations of planetary movement at least, as for
example those of precession and nutation, are involved in con-
ditions which prevent their passing a certain limit, and which in
other cases equilibrate the disturbing cause. It would seem,
therefore, contrary to analogy to suppose the case of the retar-
dation of our globe by tidal friction, whatever niay be its actual
amount, to be an exception and to go on unchecked, until the
astronomical consequences pointed out by Thomson and others
shall have occurred in the motions of our satellite, our earth,
and the sun.
VI. On some points in Mallet's Theory of Vulcanicity,
By EuG. W. HiLGAKO, University of Michigan**
THE main points of Mallet's Theory of Vulcanicity have
been before the world of science for some time, and have
excited some lively discussions on both sides of the question,
* From Silliman's American Journal^ June 18/4.
Digitized by VjOOQ IC
42 Mr. E. W. Hilgard on some points in
mainly in the English press. I think it is to be greatly regretted
that the original memoir, very tardily published in the Transac-
tions of the Royal Society, should be so difficult of access, that
few of those interested are enabled to appreciate the caution and
laborious conscientiousness which Mallet has brought to bear on
his investigation and discussion of this most complex problem^
and to what extent he has himself anticipated most of the ob-
jections raised. In calling attention to some apparent omissions
in this respect, it may be useful to recall the state of the ques-
tion as regards some of the more prominent points at issue.
The first and most sweeping attack upon the very basts of
Mallet^s theory comes from Sir William Thomson, in a letter to
Mr. Poulett Scrope (Nature, Feb. 1, 1872), in which he calls
attention to, and reaffirms the results of his investigation (supple-
mentary to that of Hopkins) on the effect which a fluid nucleus
and imperfect rigidity of the earth must exert upon precession
and nutation, and which led him to the conclusion that, unless
the rigidity of the globe as a whole were greater than that of
steel, there must ensue a tidal deformation of the solid mass,
which would sensibly change the amount of precession. He
denies that Delaunay has shaken, in any important point, the
conclusions of Hopkins or himself.
The subject has since been taken up by General Bumard
(Smithes Contr. No. 240), who, while confirming the results of
Thomson upon the premises assumed by that physicist, also
shows that there are assumable and admissible conoitions upon
which a fluid nucleus with a moderately thick crust may exhibit
the same constant, or periodically recurrent, amounts of preces-
sion and nutation as a solid globe.
Mallet refers to Thomson's argument in favour of great rigi-
dity as corroborative of the necessity for assuming a crust of
great thickness^ such as would render it inadmissible to assume
a direct connexion between volcanoes and the liquid nucleus.
But it is difficult to see how the '' preternatural rigidity,'^ made
a postulate by Thomson, could in any manner be compatible
with the requirements of Mallet's theory. For the latter repre-
sents the earth's crust as a congeries of fragments^ sustained
partly by the contracting liquid nucleus, partly by each other
on the principle of the arch — therefore necessarily often locally
in a state of unstable equilibrium, and liable to be disturbed
by slight outside forces. That the tendency to tidal deforma-
tion contributes toward producing such disturbances has been
rendered probable by Perrey's discussions, and by the repeated
coincidence of violent earthquakes with tiual extremes, lately
observed.
Thomson's assumption, that the postulated rigidity might
Digitized by VjOOQ IC
Mallet's Tl^eory of Vulcanieity. 43
result from compression, would scarcely seem admissible, save in
a case of absolute homogeneity and equilibrium — if then. It is
certainly incompatible with the demonstration made by Professor
Belli of Favia (as quoted by Mallet), to the effect that rigid
bodies are weakened by the simultaneous application of ortho-
gonal pressures — that no known materials could sustain, under
any circumstances, a strain several hundred times greater than
that which would crush it if laterally free to yield — ^that such
strains exist in the contracting crust, and that upward deforma-
tion must result, if such contraction takes place at all, as the
annual loss of heat by the earth compels us to assume is the case.
Whether we view the question of rigidity by the light of our
direct knowledge of the first twenty- five miles of crust, and of
the profound commotions it experiences from time to time, or
by that of the demonstrated increase of temperature as we de-
scend, rendering it extremely probable that at a comparatively
slight depth the rigidity of all materials must be seriously im-
paired by a high temperature despite of pressure — or whether
we even consider alone the secular loss of heat by radiation,
which must result in a contraction affecting unequally the hete-
rogeneous couches of which, on any hypothesis, the solid portion
of the earth must be composed — it will be difficult to persuade
geologists of the actual existence of the '^ preternatural rigidity ''
until every reasonable hypothesis that can dispense with this
assumption shall have been exhausted.
Among the objections raised by geologists, the first, and ap-
parently gravest, was that of Forbes (Nature, Feb. 6, 1872),
who argues the untenableness of Mallet's theory on the ground
of the asserted general identity of composition of volcanic
ejecta. In fact, from Mallet's point of view, it would seem that
lavas might have the composition of any fusible rock whatso-
ever in whose strata the crushing might happen to occur, and
hence that, if taking place within the sedimentary strata, there
ought to be a very great diversity between the ejecta of different
vents.
In his rejoinder Mallet calls attention to the very serious dif-
ferences of composition between the extremes of trachytic and
basaltic lavas, and to the generally admitted fact that volcanoes
are located along axes of upheaval, where the hypogene rocks,
and therefore those of the crust proper, approach the sur-
face— hence that crushing along these lines of weakness would
be by no means likely to produce a greater diversity of lavas
than we actually observe. Furthermore, that the ^' local lake "
theory is liable to the same objection, unless the lakes are sup-
posed to be located within the (uniform) crust itself.
He might, it seems to me, have added that the maximum of
Digitized by VjOOQ IC
44 Mr. E. W. Hilgard on some points in
twenty-five miles of sedimentary rocks is not anywhere (on the
continental areas at least) actually superimposed vertically upon
the crusty and hence that it is not unreasonable to assume
that a pressure sufficiently great to produce fusion may never
occur within the limits of the sedimentary strata^ albeit other
manifestations of subterraneous thermal action may not be
wanting. It is true that^ on the whole, Mallet's memoir leaves
upon the reader's mind the impression that he seeks the source
of volcanic action at depths sufficiently shallow to justify in a
measure the objection raised by Forbes, although he ex-
pressly declares that, with our present data, the determination
of the points at which the maximum of crushing-effects occurs
is impossible.
Similar considerations apply to the objection raised by P. W.
Button (Nature, Nov. 27, 1873), that *Maults show no heating-
effects, even where considerable crushing has taken place.''
The pressure under which the faulting occurred may have been
inadequate, in the cases coming under our observation; but
above all, time is a most essential element in this connexion.
No matter how great the dislocation or crushing, no great in-
crease of temperature can occur if it takes place slowly , however
great may be the quantity of work performed, or of heat pro-
duced. And very many, if not the majority of extensive faults
actually occurring, show evidence of having been formed without
cataclysmal disturbance.
Among the other points raised by Hutton {loc. cit.) there are
several which are at once disposed of by a perusal of the original
memoir. There are others of some weight. That ^' lines of
least resistance once chosen must remain," is doubtless true in
a very wide sense ; and in that sense this is scarcely at variance
with observed facts, since the lines of weakness along the bor-
ders of continents are still those which exhibit volcanic activity
(and earthquake phenomena) most frequently. But in the fold-
ing and upheaving of strata by tangential thrust the question
of equilibrium must often*of necessity be very delicately balanced,
depending as it does upon the vertical pressure of the masses^
their nature, dislocation, subsequent consolidation, igneous
effusions from iissures, &c. Lines of weakness as to rigidity
may thus easily acquire sufficient static resistance to cause a
subsequent yielding to take place at some distance from the
original axis, as is exemplified in the formation of successive
parallel ranges. What is true with regard to the formation of
folds is equally so as concerns the settling down of the crust-
fragments in consequence of interior contraction. Each frag-
ment as a whole may remain as such, being only, as it were,
abraded at its circumference. But it is only necessary to have
Digitized by VjOOQ IC
Mallet^s Theory of Vulcanicity. 46
observed the gradual yielding of detrital rock-masses under pres-
sure^ to understand why the cataelysmal yielding which mani-
fests itself in earthquakes should so frequently change its locality
of occurrence — why for long periods a region may be completely
exempt from these movements^ in consequence either of an un-
resisted and therefore gradual descent of the crust-fragments
underlying it, or of an arch-like arrangement, whose sudden
breaking down will result in a catastrophe, succeeded perhaps
by a long period of quiescence.
Thus Mallet^s theory accounts equally well for the sporadic
and apparently lawless occurrence of seismic phenomena, and
for the probable correlation between the frequency and violence
of earthquakes and tidal extremes. Unlike the theory of a thin
crust, which would lead us to expect almost diurnal earthquakes
corresponding to oceanic tides, according to Mallet's view there
should be a near coincidence in time and space of two indepen*
dent factors (viz. of a condition of very unstable equilibrium of
some crust-fragment, with a tidal extreme) in order to produce
a maximum of disturbance. It cannot be expected that such
coincidence should be of frequent occurrence, or that the casual
connexion should manifest itself in a greater predominance than
that claimed by Perrey for the times of spring and neap tides.
Mallet does not, however, allude to this point — whether from a
distrust of Perrey's data and method, or theoretical scruples on
the score of " rigidity .''
The objection, that according to Mallet's theory earthquake;?}
ought always to be followed by eruptions, could obviously
apply only during the period of fissure eruptions from the
liquid interior — it being conceded that the volcanic eruptions
of to-day are due to contact of water with the molten rock, and
that steam, not static pressure, is the vis a tergo. It is, of
course, very probable that the access of water to the volcanic
focus* is generally caused or facilitated by such crust-move-
ments as would at the same time result in the production of
more heat and perhaps of fused rock, such movements being
indicated by the (mostly slight) earthquakes that so frequently
precede a period of volcanic activity. Hutton's objection, that
according to Mallet's view each eruption ought to be preceded
by a sensible subsidence, is therefore groundless.
One point, however, must strike every reader of the original
memoir, viz. the preeminence given by Mallet to the crushing of
solid rock as the means of producing heat and fusion. Que
would naturally look to the results of his experiments on this
♦ Hut ton {loc. cit,) avers that " to cause a volcano the heat must go to
the water ; the water cannot go to the heat>" but omits any explanation of
this singular axiom.
Digitized by VjOOQ IC
46 Mr. E. W. Hilgard on some points in
subject for the proof of the efficiency of this agency. But we
find that the maximum of temperature resulting from the crush-
ing to powder* of the hardest rock is something over 217^
Fahr. This, then, represents the maximum increment of tem-
perature that can be rendered efficient toward the fusing of
rocks by the crushing process under the most favourable cir-
cumstances, viz. upon the supposition that it takes place in-
stantaneously, or under such circumstances that the heat can-
uot be conducted away, and, further, that the resistance of the
rock has not been materially diminished by the downward in-
crease of hypogeal temperature. At the most moderate depths
at which volcanic phenomena can be supposed to originate, the
last-mentioned factor must exert a very considerable influence,
reducing mateiially the available heat-increment. Hence the
numerical results of Mallet's laborious experiments on rock-
crushing, however interesting and useful as affording a definite
measure of the thermal effects producible by this means, yet
fail to carry conviction as to the efficacy of this particular modus
operandi in reducing large masses of solid rock to fusion, unless
essentially supplemented by friction, not so much of rock walls
against each other, but more probably by the heat produced
within more or less comminuted detrital or igneoplastic masses
by violent pi'essure and deformation.
It may be doubtful what would be the physical and thermal
effect of enormously great pressures upon rock powder such as
was produced in Mallet's experiments ; but it would seem that
if made to yield, the frictional effect must produce very high
temperatures. A fortiori, solid detrital masses of variously
sized fragments intermingled (such as, rather than powder,
would be likely to result from steady pressure), yielding rapidly
under great pressures, might, under the combined influence of
friction and rock-crushing, well be supposed to reach the tempe-
rature of fusion, which a simple crushing of a solid mass by
pressure would have failed to produce. Mallet mentions the
probable influence of friction, and of the squeezing of igneo-
plastic masses, but does not attach to these agencies such im-
portance as they seem to me to deserve.
Of the complex thermal effects of the movements of detrital
masses under great pressure. Mallet's figures of course offer no
measure whatsoever ; nor is this, or even the thermal coefficients
resulting from his rock- crushing experiments, at all necessary
to the establishment of the postulates of his theory.
* Mallet does not go into the consideration of the physical nature of this
" powder," and of the thermal and other differences likely to result from
its production under pressures enormously greater than those employed
by him.
Digitized by VjOOQ IC
Mallet's Theory of Vtdcamcity. 47
Taking for granted the correctness of Hirn's theorem, '^ that
the heat evolved in the crushing of rigid bodies is the equiva-
lent of the work performed/' Mallet's experiments on the con-
traction of fused rock in cooling, and his estimates of the amount
of volcanic energy manifested on the globe, coupled with that of
the earth's annual loss of heat, completed the proof of the qimu'
titative adequacy of the cause invoked by him. And when it is
understood that the earth's present loss of heat during sixteen
and a half years is the mechanical equivalent of all the volcanic
work performed since the period of fissure eruptions, the burthen
of proof of the qualitative inefficiency of the several modes of
action that may come into play would seem to be effectually
thrown upon the opponents of the theory.
Among these modes of action, the fusion of masses already
existing in a pasty, or generally more or less igneoplastic con-
dition, by squeezing or forcible displacement, seems to me to
deserve especial attention. At the depth at which volcanic
phenomena must be supposed to originate, this condition must
be closely approached, especially in the early times of the vol-
eanic period — that of the '^ Maare " of the Eifel and other simi-
lar cases representing the transition phase between the regime
of fissure-eruptions and that of volcanoes proper. In this
period of a ^ greatly stiffened and thickened crust,'' even slight
flexures, whether synclinal or anticlinal, would occasion great
displacements and movements in the half-stiffened upper layers
of the "viscous couchc/' and if these experienced local re-
fusion, the fused matter may well be presumed to have often
been disposed of by eruption through fissures or volcanic vents,
rather than by overcoming downward the inertia of the viscous
couches* This mode of action seems to me likely not only to
afford a more copious, but also a more constant or lasting source
of supply than the supposed crushing of solid rock, and appears
especially applicable to the case of large fissure-eruptions.
Among the greatest services rendered by Mallet's (or, in this
connexion, Wurtz's) theory is the unstrained explanation of
many of the phenomena of mctamorphism that were quite un-
intelligible so long as the heat required for the observed
changes was supposed to be derived from below, and perhaps
by transmission through strata which themselves bad experi-
enced little or no change of condition. The principle that the
heat evolved in the flexure or forcible compression of strata is,
cateris paribus, proportional to the resistance offered by them
to the external force, throws a flood of light upon numerous
apparently contradictory phenomena, which have long been
quoted as incompatible with the doctriue of metamorphism as
held in this country, and have stood in the way of its general
Digitized by VjOOQ IC
48 Mr. £• W. Hilgard on some points in
acceptance by geologists, particularly on the continent of
Europe. In its application to the formation of synclinoria
especially, the principle works most instructively and satisfac-
torily. It can scarcely be doubted that in the first folding of
the vertex of a geosynclinal^ weakened below by fusing away
and heating of the crust and lowest strata, the movements
were comparatively localized and rapid, and therefore capable
of producing high temperatures, and their results such as we
now usually find them along the main axes of elevation of syn-
clinoria. But as the resistance along this axis increased by
emergence and solidification, the points of yielding (t. e, the
folds) would be muli^lied, while the absolute amount of motion
transformable into heat would be diminished in each. Hence
the decrease in general of metamorphic effects as we recede
from the main axis. And yet it is perfectly easy to conceive
of large local exceptions to the general rule (such as we actu-
ally observe), on the basis of greater resistance in perhaps a
localized stratum of a lateral fold, yet so situated that it could
not successfully resist the influence of an advantage of leverage
causing a rapid deformation. It is even predicable that under
such circumstances sudden breaks and crushings must occa-
sionally have occurred, giving rise to fusion of rocks and limited
fissure-eruptions, or at least to pasty rock intrusions — as sug-
gested by Dana for granitic and analogous veins^ that show no
evidences of the cooperation of very high temperature in the
act of formation.
LeConte's view, that the first mashing of a geosynclinal
would produce less heat than later plications*, in which (pre-
sumably) a greater resistance would have to be overcome, seems
hardly to be compatible with facts as generally observed away
from the Pacific-coast eruptions ; and his argument is the less
cogent, as the temperature produced is a function, not only of
the resistance of the rocks, but also of the degree and rapidity
of the motions, both of which have been on the decrease in late
geological periods^ in accordance with the diminishing rate of
contraction of the earth and the increased resistance of the crust
to flexure.
While Mallet's theory accounts satisfactorily for earthquake
phenomena and volcanic activity as manifested since the cessa-
tion of fissure-eruptions, and also for the gradual or sudden
depression of both large and small areas even subsequent to
that time, it makes no provision for their elevation, and there-
fore leaves unexplained the numerous oscillations of level of
which we find the record down to our own time. In assuming
* " On the great Lava-flood of the West«'* Silliman's American Journal,
March 1874, p. 179.
Digitized by VjOOQ IC
Mallet's Theory ofVukanieity. 49
the movements as taking place exclusively within the solid
shell, he (unnecessarily as it seems to me) leaves a point open
to obiection.
While admitting that slow secular oscillations, or those minor
changes of level constantly occurring in volcanic areas, may
even now in many cases be reasonably attributed to changes of
temperature occurring within the solid rocks themselves, and
within their limits of elasticity, it is impossible to assign this
as an adequate cause of those extensive oscillations which
have characterised the Quaternary period, and are recorded,
€. g.y by the raised beaches of the North-Atlantic coasts and
inlets, and by the drift-pebbles even now found four hundred
and fifty feet below the level of the Gulf of Mexico, while the
emerged formations record a complementary elevation to at
least a similar extent during the Terrace epoch. This record
of an oscillation of near a thousand feet on the Gulf-shore
since the glacial-drift epoch, implies at least a corresponding one
over the greater portion of the area drained by the Mississippi,
unless that river flowed backward at one time*. Doubtless
these oscillations, like the glaciation of which they probably
were cooperative causes, were of continental extent, as was the
(more or less contemporary) emergence of the Siberian plain ;
and as such they must be presumed to have been true move-
ments of the earth's crust, although lying quite within the vol-
canic period proper. It is but reasonable to suppose that the
sinking of the great Pacific area was then, and may still be,
of a similar nature.
If Mallet's theory, as well as the geological facts with which
it deals, is incompatible with Hopkins's and Thomson's postu-
late of extreme rigidity ; if, as it appears to me, the events of
very recent geological epochs in connexion with the very slow
rate of cooling since that time render it unlikely that the crust
can even now be considered rigid in a geological sense; if^
finally, as General Barnard affirms, the astronomical objection to
a comparatively pliant crust and liquid nucleus is not absolute,
* It is a cunous fact that in the vaiious hv pothenes regarding the oscil-
lations of the continental interior during tlie Drift epoch, the facts ob-
served on the Gulf-shore have over and again been quietly ignored,
although the Gulf is unequivocally the natural reference-level most directly
related to that interior, not only at the present time, but; as the direction
of the Drift currents and the trend of the formations show, ever since the
time of the Cretaceous emergence. Nevertheless the reference- level has
been sought bevond the Alleghany upheavals, or beyond the fixed Azoic
area upon which the movement appears, in a measure, to have pivoted,
and wnere, as Dana has shown, it was materially diminished in extent.
Assuredly no hypothesis which disregards the changes of level registered
at the continental outlet has any raison (Petre !
PhU. Mag. S. 4. Vol. 48. No. 315. July 1874. E
Digitized by VjOOQ IC
50 Mr. B. W. Hilgard on some points in
but may be obviated by admissible assumptions regarding the
mode of distribution of the solid and liquid matter constituting
the globe^ — ^we are led to the reasonable assumption that while
the thickness and rigidity of the crust is evidently too great to
admit of further folding or fissure-eruptions^ and (probably) to
admit of connecting ordinary volcanic phenomena directly with
the (virtually or actually) liquid interior^ yet we need not as-
sume it to be so great as to render the crust incapable of yield-
ing somewhat^ on a large scale, to static upward pressure. Such
pressure may be either the resultant of tangential stress^ such
as might slightly deform an arch without fracture or folding,
or even the direct result of a corresponding subsidence else-
where.
The latter effect would of course be incompatible with a
shrinking away of the fluid interior &om the crusty as required
by Mallet's theory^ if it were necessary to assume that the in-
terior crust-surface is substantially '^ smooth/' t. e. free from
important downward projections or upward sinuosities. But so
far from this, the cooling influence that has so long acted on
the oceanic areas, contrasted with those enormous outwellings
of igneous rock that have occurred even in late Tertiary or
Posttertiary times, together with other considerations, necessi-
tate the assumption that such inequalities do exist to a notable
extent. Hence the overlapping alluded to by Mallet of the
period of fissure-eruptions and of that of volcanic activity
proper, which appear to have coexisted, in different portions of
the globe, from early Tertiary to early Quaternary times. For
even Mallet himself considers the outpourings of igneous rocks
on the Pacific coast "wholly inconsistent with existing vol-
canic forces/' and few geologists will agree with LeConte* in
ascribing precisely these most extensive fissure-eruptions in the
world to the " ineffectual fires '' of the volcanic period, arising
alone from transformed motion.
Indeed it is not easy to understand the precise mechanism
of the great fissure-eruptions as a consequence of nucleal con-
traction, without the aid of some static head of pressure that may
exist more or less locally, in consequence of inequalities in the
crust (whether of form, thicknessi or density), and thus act as
Si vis a tergo.
At first blush the '' squeezing out of sub-mountain liquid
matter," assumed by LeConte as the consequence of the fold-
ing and fissuring of strata by tangential thrust, appears natural
enough. Yet it seems hardly possible that the same force
which makes and elevates mountain folds (being the result of
interior shrinkage) should at the same time serve to compress the
* SiUiman's American Journal, March 1874, p. 1/9.
Digitized by VjOOQ IC
Malleus Theory of Vuiamkiiy. 51
wUerior Uqwii, xuaikm either sueh folding oeeon benealh tke
g^Mral k^ of the liquid, or the latter is locally confined,
or the morement is so (comparatively) brusque or cataclysmal,
that viscosity would prevent the lateral or downward escape of
the liquid rock. In the case of the Pacific eruptions the evi-
dence of steady static outflow and regular upbuilding is espe-
cially eogent; and, as LeConte remarks, it has been ^ow work,
as indeed is usually or universally the case with mountain*
building'^*
The assumption of locally limited fire seas with a solid globe
as made by Danaf in conformity with Hopkins's views, would
remove the difficulty if the ^rust ocrald be assumed as contract-
ing on the whole independently of the portions over fire seas.
But when we come to discuss the appUcation in detail of this
intrinsically improbable hypothesis, we find the required ex-
tent and localities of these fire seas to be such that we can
hardly imagine them to be eflfectually separated from eaeh
other; in other words, we approach very near to a condition of
general undercrust fluidity up to late geological periods j:. It
then becomes a question of minor importance whether there is
a central nucleus solidified by pressure, or whether all within
the crust is actually liquid.
The inherent improbability of the depression of a ^eosyn-
dinal trough to a level so low as to allow the liqmd rock
to rise into t/, as it were, is too great to render its discussion
necessary.
Indeed it seems almost impossible to imagine a mechanism
explaining satisfactorily fissure-eruptions such as those of the
Pacific coast, on the basis of a slowly contracting 9oHd crust
with a rapidly contracting liquid layer or nucleus beneath. A
more satisfactory explanation seems possible if, in accordance
with Mallet's suggestion and the intrinsic probabilities of the
* When LeConte savs {loe, cit, p. 179) that the outoqueezing of the
liquid hai been caused by " enormous horizontal pressure, determined by
the interior contraction of the whole earth," and then (p. 180) that,
^ whether by uplifting or upbuilding the actual increase of height would
be precisely the same, being detennmed by the amount of kteral crush-
ing,'' he seems to think of crust-oontrac^on upon a nucleus too large for
it, rather than of Mallet's " freely descending " crust. Or, if he considers
the fused rock the result of motion transformed, it is difficult to see on
what ground a simple ** uplifting " could be considered the precise mecha-
nical equivalent of an upbuilding by eruption of Uquid rock. In either
ease the UfHng done would be the same ; but what of the enormous heat
qffiuianl
t " On some of the Results of the Earth's Contraction," Silliman's
American Journal, August 1873, p. 105.
t Ibid. July IB73, p. 7 et seqq.
E2
Digitized by VjOOQ IC
63 On game pdiaU in Maliet's Theory of VulcanieUy.
case, we as^ame the existence of a thickly viscid/ igneoplastic
uodercrnst layer. Such a byer, while barely or very slowly
obeyine the laws of li(^uid equilibrium, would be capable of
being liquefied by a slight increase of tCDiperature, such as
might be produced by squeesing or kneading. Portions of
such plastic matter would occasionally become involved in the
anticlinal folds of syndinoria, and thus supply the material for
limited fissure-eruptions, in that case literally '* squeezed out."
But the inverse ratio pointed out by Dana as existing between
folding and fissure-eruptions points to the rarity of such
events.
At any rate they could not explain the outwellings of the
Pacific border^ which continued long after close plications had
ceased to be made — in fact, as it would seem, up to the end of
the period of elevation of the main Sierra Nevada.
It is but fair to assume that near lines of weakness indicated
by plications or fissure-eruptions, the isogeotherms have been
during the elevation of mountain-chains (and probably still are
where such lines are marked by volcanic vents) considerably
above their general leveL In an anticlinal upheaval they
would probably conform to the progress of the sublevatory
movement, in a ratio more or less directly proportional to the
rapidity of the upward movement, and would gradually descend
during periods of repose. This would happen independently of
any heat generated by transformation of motion.
In a polygenetic chain Uke the Sierra Nevada, after the coU
lapse and folding of the geosynclind and the subsequent stif-
fening of the backbone (so to speak), any further elevation of
the main ridge becomes a ^tioM-anticlinal movement, accom-
panied necessarily by the compression and " squeesing " of the
heated rocks embraced within the arch. The heating being
greatest, aeteris paribus, where the resistance and motion is a
maximum, more heat would be generated by the compression
of the upper, half-stifiened portion of the viscous or igneoplastic
layer, than in the lower ones ; and the liquid matter so formed
would constitute a head of pressure, from which fissure-erup-
tions might derive their material ; whether directly, or by pres-
sure communicated to more distant points of rupture and fusion
by lateral stress.
If, then, as LeConte^s data seem to show, the final and most
considerable anticlinal elevation of the great interior range took
place during the same period that witnessed the great fissure-
eruptions of the Coast and Cascade ranges, it may not be un-
reasonable to suppose these events to have not only been con-
temporaneous, but to have borne to each other something of
the relation of cause and effect, and that each of the numerous
Digitized by VjOOQ IC
On a New Formula inDefinite Integrals* 53
saperimposed strata of igaeoas rock in the latter region may
represent not only the direct effect m loco of more or less par-
oxysmal thrusts^ but also the reflex action of the simultaneously
progressing anticlinals in the high Sierras.
VII. A New Formula in Definite Integrals.
By J. W. L. Glaishbr, M.A*.
1. 1 NT£6BATE the identity
^-«i^+^----=i+^-^^(I^« + ^'^0(^ (1)
(where Aa«=:a»4.|~a») between the limits zero and infinity^ and
the right-hand side becomes
w
= 1 (flocos*^— Aflotan«tfcos*tf+.,.)»«c*ft»
w
= r'(flro- Atfo Bin* tf + A«flo sin* tf- . . .)d0
'tA 1 a . 8 1 .o 5 8 1.- \
so that
i
The definition of the symbol E is contained in Ea«=:a»4.i ; and
of course, a^ being only defined for n a positive integer, a.| is
without meaning. But in cases where On involves factorials,,
there is a strong presumption, derived from experience in similar
questi9us, that the formula will give correct results if the conti-
nuity of the terms is preserved by the substitution of gamma
functions for the factorials. This I have found to be true in
every case to which I have applied (2).
* Commmiicated by the Author.
Digitized by VjOOQ IC
64 Mr. J. W. L. Olaisher an a New Formula
E.ff.{\) Let
1.2...(2n+l)"r(2n+2) '
then a-.^=l^ and
i
which is true,
(u) Let
then
and
the true result.
"'" 1.2...» ~ r(n+l)'
a-i 1
^ '* *^* «•- n^n = rWTT)' '• ^•^
X
coBoadx^iO,
TU. sin oossOj the value we should expect to find by any process
that gave a result at all.
2. Divide (1) by 1+^ and integrate as before: the right-
hand side
w
= j (aoCOs«^-Afli>sin«^cos«^+A*aown*^cos«d— ...)iW
TT/l 1 1 A . 8 1 1 .o 5 8 1 1 ..^ \
= 2(2"4-2^+6-4-2^-5-r4-2^+---;^
•wv/ITA— 1^ _*»r 1
2 A ''^"2l+-v/E^'
so that
Take
«*• ^
1.2...2n r(2n+l)'
Digitized by VjOOQ IC
in Definite Integrak. 55
and
J. i+i«'^=2(i-''+r:2---r2''- • • (*>
Similarly, by taking a»=s ^ , we obtain the correct value of
® X sin ax ,
or.
I
The peculiarity of (2) and (3) consists in the appearance on
the right-hand side of terms with fractional arguments. In such
an equation as (4), where one side is a function of a^, while the
other involves uneven powers of a, it seems as though it would
be impossible to evaluate the integral by any direct procedure;
for d priori it would appear that no method of expansion and
integration term by term could transform a function of (f
into one of a, and thus, as it were, extract the square root
of a constant involved. The way in which the symbolic pro-
cess introduces i/£, and so actually does effect this conver-
sion, is interesting: when I first applied the identity (1) to
the integral in (4), I scarcely expected to obtain any result
capable of interpretation.
Whenever (2) and (3) admit of interpretation, it is highly pro-
bable that the result so given will be the true one ; e. g., taking
1 +««'**- 2 lr(i) r{|) ^ r(2) r(5) +• * •/
_ir r 2a* . 2at «« \
~2L v^A 1.3 1.8-6 //
the known vslae. Bat (2) and (3), as general formule, are re-
markable ; and diey would give results in very many cases where
it might not be easy to evaluate the integrals otherwise. |
Trinity College, Cambridge,
June 19, 1874.
Digitized by VjOOQIC
[ 56 ]
VIII. On some Physical Properties of Ice; on the TVansposition
of Boulders from below to above the Ice ; and on Mammoth"
remains. By John Rae, M,D,, LL.D., ifc*.
IS the ice formed on salt water fresh f or, in other words, if
ice formed on the sea is thavred, will the water obtained
thereby be fresh ?
For a number of years past I have spoken with many persons
on the above subject; and seldom » if ever, have I found a single
individual who did not say that the ice of the sea was fresh.
Some of these gentlemen are known in the scientific world ;
and many of them supported their opinions by quoting the
highest written authorities on the subject, chiefly Tyndall's
'Forms of Water,' p. 132, par. 339, which tells us that "even
when water is saturated with salt, the crystallizing force studi-
ously rejects the salt, and devotes itself to the congelation of
the water alone. Hence the ice of sea-water, when melted, pro^
duces fresh water,"
It IS the sentence in italics to which I wish to draw particular
attention.
It would be the extreme of folly and presumption on my
part to question the correctness of results obtained b^ scientific
men in their experiments in freezing small quantities of sea-
water by artificial means, more especially those of the distin*
guished gentleman whose name I have mentioned, who, in
addition to holding the high position of being one of our
greatest authorities in all that relates to physical science, pos-
sesses the rare gift of being able to communicate his knowledge
in such plain, clear, and forcible language, illustrated by admi-
rable experiments, as to make his meaning fully understood,
even by those who had previously been perfectly ignorant of
the subject.
It is only where I have had opportunities of witnessing the
action of cold carried on in a manner which may have been
denied to the scientific man, that I venture to differ from him ;
and it is in this way that the conviction has been forced upon
me, that the ice of sea-water if melted does not produce finesh
water.
Before entering upon this subject, however, let me say a word
or two on the first part of the quotation I have given.
If a saturated solution of salt is frozen, and the ice so formed
is fresh, it is evident that the salt that has been ''rejected'^
must be deposited or precipitated in a crystalline or some other
solid form, because the water, if any, that remains unfrozen,
* Read before the Physical Society, May 9, 1874. Gommunicated by
the Society.
Digitized by VjOOQ IC
Dr. J. Rae an same Physical Properties qflce. 57
h&ng already saturated^ can hold in solution no more salt than
it already contains.
Could not salt be obtained readily and cheaply by this means
from sea- water in cold climates ?
During several long journeys on the Arctic coast^ in the early
spring before any thaw had taken place^ the only water to be
obtained was by melting snow or ice. By experience I found
that a kettleful of water could be obtained by thawing ice with
a much less expenditure of fuel^ and in a shorter time, than
was required to obtain a similar quantity of water by thawing
snow. Now, as we had to carry our fuel with us, this saving of
fuel and of time was an important consideration, and we always
endeavoured to get ice for this purpose. We had another in-
ducement to test the sea-ice frequently as to its freshness or
the reverse.
I presume that almost every one knows that to eat snow
when it is very cold, tends to increase thirst, whereas a piece of
ice in the mouth is refreshing and beneficial, however cold it
may be ; we were consequently always glad to get a bit of fresh
ice whilst at the laborious work of hauling our heavy sledges ;
yet with these strong inducements we were never able to find
sea-ice, in situ*, either eatable when solid or drinkable when
thawed, it being invariably much too salt. The only exception
(if it may be cidled one) to this rule, was when we found rough
ice, which, from its wasted appearance and irregular form, had
evidently been the formation of a previous winter. This old
ice, if projecting a foot or two above the water-level, was almost
invariably fresh, and, when thawed, gave excellent drinking-
water. It may be said that these pieces of fresh ice were frag-
ments of glaciers or icebergs ; but this could not be so, as they
were found where neither glaciers nor icebergs are ever seen.
How is this'to be accounted for? Unfortunately I have only
a theory to o£fer in explanation.
When the sea freezes by the abstraction of heat from its
surface, I do not think that the saline matter, although retained
in and incorporated with the ice, assumes the soUd state, unless
the cold is very intense, but that it remains fluid in the form of
a very strong brine enclosed in very minute cells. So long as
the ice continues to float at the same level, or nearly the same
level, as the sea, this brine remains ; but when the ice is raised
a little above the water-level, tbe brine, by its greater specific
gravity, and probably by some solvent quality acting on the ice,
gradually drains off from the ice so raised; and the small cells,
*■ What I mean by ice mi situ is ice lyin^ flat and unbroken on the
sea, as formed during the winter it is formed m.
Digitized by VjOOQ IC
58 Dr. J. Bae on the IVaMpoiitum ofBoulden
by eonnecting one with another downwards^ become channek of
drainage.
There may be seTeral other requisiteB for this change of salt
ice into fresh^ sach as temperature raised to the freezing-point,
so as to enable the brine to work out the cell-walls into channels
or tubes — that is^ ifmy theory has any foundation in fact, which
may be easily tested by any expedition passing one or more
winters on the Arctic, or by any one living where ice of con*
siderable thickness is formea on the sea, such as some parts of
Norway.
All that is required, as soon as the winter has advanced £sr
enough for the purpose, is to cut out a block of sea-ice (taking
care not to be near the outflow of any fresh-water stream) about
8 feet square, remove it from the sea to some convenient posi-
tion, test its saltness at the time, and at intervals repeat the
testing both on its upper and lower surfiEU^es, and observe the
drainage if any.
The result of the above experiment, even if continued for a
long while, may not be satisfactory, because the fresh ice that I
have described must have been formed at least twelve months^
perhaps eighteen months, before.
The JVanapoeition of Boulders from below to above the lee.
When boulders, small stones, sand, gravel, 8cc. are found
lying on sea-ice, it is very generally supposed that they must
have rolled down a steep place or fallen from a clifi*, or been
deposited by a flow of water firom a river or other source.
There is, however, another way in which boulders &c. get upon
floe-ice, which I have not seen mentioned in any book on this
subject.
During the spring of 1847, at Bepulse Bay. on the Arctic
shores of America, I was surprised to observe, after the thaw
commenced, that large boulders (some of them 3 or 4 feet in
diameter^ began to appear on the surface of the ice; and after a
while, about the month of July, th^ were wholly exposed,
whilst the ice below them was sttong, nrm, and something like
4 feet thick.
There were no clifls or steep banks near from which these
boulders could have come ; and the only way in which I could
account for their appearance, was that which by subsequent
observation I found to be correct.
On the shores of Bqpulse Bay the rise and frdl of the tide
are 6 or 8 feet, sometimes more. When the ice is forming in
early winter, it rests, when the tide is out, on any boulders &c.
that may be at or near low-water mark. At first, whilst the
Digitized by VjOOQ IC
fmm behw to above the Ice. 59
ice 18 weak, the boalden break through it ; but whea the ice
becomes (say 2 or 3 fe^) thick, it freezes firmly to the boulder,
and when the tide rises, is strong enough to lift the boulder
with it. Thus, once fastened to the ice, the stone continues
to riae and fall with the rise and fall of ^ush tide, until, as the
winter advances, it becomes completely enclosed in the ice,
which by measurement I found to attain a thickness of more
than 8 feet
SmaU stones, gravel, sand, and shells may be fixed in the
iee in the same way.
In the spring, by the double efiisct of thaw and evaporation,
the upper surface of the ice, to the extent of S feet or more, is
removeidy and thus the boulders, which in autumn were lying
at the bottom <tf the sea, are now on the ice, while it is stiU
strong and thick enough to travel with its load, before favour-
able winds and currents to a great distance.
The finding small stones and gravel on ice out to sea does not
always prove that such ice has been near the shore at some time
at other.
I have noticed that wherever the Walrus in any numbers
have been for some time lying either on ice or rocks, a not
inconsiderable quantity of gravd has been deposited, apparently
a portion of the excreta of that animal, having probably been
taken up from the bottom of the sea and swallowed along with
their food.
Mammoth'remaiM. The position in which their Skeletons are
found, Sfc,
In LyelFs ' Principles of (Geology,* vol. i. p. 186, we read ^—
''In the flat country near the mouth of the Yenesei river,
Siberia, between latitudes 7(f and 75*^ north, many skeletons of
mammoths, retaining the hair and skin, have been found. The
heads of most of these are said to have been turned to the south/'
As fsur as I -can find, the distinguished geologist gives no
reason why the heads of the mammoths were turned to the
south ; nor does he say all that I think might be said of the
reasons why, and the means by which the skins have been pre-
served for such a long period of time.
Having lived some years on the banks of two of the great
rivers of America, near to where they enter Hudson's Bay, and
also on the M'Kenzie, which flows into the Arctic Sea, 1 have
had opportunities of observing what takes place on these streams^
all of which have large alluvud deposits, forming flats and shal«
lows at iheir mouths.
What I know to be of common occurrence in these rivers
may, if we reason by analogy, have taken place in ancient timea
Digitized by VjOOQ IC
60 Dr; J. Rae on Mammoth-remains.
on the great rivers of Siberia, making due allowance for the
Dincb higher northern latitude to which these streams run before
reaching the sea, and for the difference in size of the fauna that
used to frequent their banks.
When animals, more especially those having horns, tusks, or
otherwise heavily weighted heads, are drifting down a riv^,
the position of the bodies may lie in any dir^ion as regards
the course of the stream, as long as they are in water deep
enough to float them ; but the moment they get into a shallow
place, the head, which sinks deepest (or, as sailors say, ^^ draws
most water *'), takes the ground, whilst the body, still remaining
afloat, swings to the current, just as a boat or ship does when
brought to anchor in a tideway.
It is probable that the mammoths, having been drowned by
breaking through the ice or in swimming across the river in
spring when the banks were lined with high precipitous drifts
of snow, which prevented them from getting out of the water,
or killed in some other way, floated down stream, perhaps for
hundreds of miles, until they reached the shallows at the mouth,
where the heads, loaded with a great weight of bone and tusks,
would get aground in 8 or 4 feet of water, whilst the bodies
still afloat would swing round with the current as ahready
described.
The Yenesei flows from south to north, so the heads, being
pointed up stream, would be to the south*.
Supposing, then, these bodies anchored as above in 8 or 4 feet
water ,* as soon as the winter set in, they would be frosen up in
this position. The ice in so high a latitude as 70^ or 75^ north
would acquire a thickness of 5 or 6 feet at least, so that it would
freeze to the bottom on the shallows where the mammoths were
anchored. la the spring, on the breaking np of the ice, this
ice being solidly frozen to the muddy bottom, would not rise to
the surface, but remain fixed, with its contained animal remains,
and the flooded stream would rush over both, leaving a covering
of mud as the water subsided.
Part of this fixed ice, but not the whole, might be thawed
away during summer ; and (possibly, but not nec^sarily) next
winter a fresh layer of ice with a fresh supply of aninial re-
mains might be formed over the former stratum ; and so the
peculiar position and perfect state of preservation of this ini«
* Not many yean ago, when buiblo were very abundant on the Saskat*
chewan, hundreds of them were aometimea drowned in one seaaon whilat
awimming acroaa the river; and many reindeer, mooae, and other animala
are annually destroyed in Uiia way in other large American rivers.
Sir Charlea Lyell mentiona a number of yaka being aeen frozen up in
one of the Siberian rivers, which, on the broking up of the ice in apnog,
would be liberated and float down the alream.
Digitized by VjOOQ IC
Mr. F. Clowes on a Glass Cell with Parallel Sides. 61
menae collection of extinct animals may be accounted for without
having recourse to the somewhat improbable theory that a very
great and sudden change had taken place in the climate of that
region.
I have seen at the mouth of Hayes River in America animals
frozen up as above described ; but as the latitude of this place is
only 57^ norths the fixed ice usually wholly di8apf>ear8 before
the next winter sets in, and liberates the animals shut up in it ;
but when the rivers reach the sea, as some of those of Siberia
do, 1000 or 1200 miles further to the north, it may be fairly
assumed that a large part of this fixed ice, protected as i would
be by a layer of mud, might continue unthawed.
IX. Glass Cell with Parallel Sides.
By F. Clowes, Esq., B.Sc, F.C.S.*
THE following method has proved very convenient for making
a glass cell, which may be readily fitted up from ordinary
laboratory apparatus, and may also be rapidly taken to pieces
for the purpose of being cleansed.
A piece of india-rubber tubing with stout walls, or, better, a
length of solid rubber, is placed pig. | .
in the form of a letter iJ be-
tween two plates of glass, the
ends of these plates being then
firmly held together by slipping
over them stout in<ua-rubber
rings. A glass cell is thus obtained, the parallel faces of which
are formed by the glass plates, whilst its thickness, depth, and
length can be suitably varied by the stoutness and length of the
rubber tube and the shape which this tube is made to assume.
With a glass cell of the size of an ordinary magic-lantern
slide (fig. 1), thedifierence in specific gravity between hot and
cold water t may be well shown upon the screen by a magic
lantern, the liquid admitted by a pipette being preferably tinged
by dissolving in it a crystal of potassium permanganate ; and
the convective currents occurring in the mass of a liquid may be
thrown upon the screen by passing a galvanic current through
a fine platinum wire stretched between two thick copper wires
beneath the surface of the liquid in the cell : these currents are
rendered much more evident by allowing the platinum wire to
be immersed in a stratum of potassium -permanganate solution
which has been cautiously introduced beneath the water by
means of a pipette dipping to the bottom of the cell.
* Read before the Physical Society, May 23, 1874. Communicated by
tile Socdetv*
t See iVndairs 'Heat, a Mode of Motion,' pp. 173 and 174.
Digitized by VjOOQ IC
flHF
H
^^1
d3 Noticet r$tj9eeHng New Books.
A smaller cell made to fit into the wooden firame o( a kntern-
riide (fig. 2), which has attached Fig. 2.
to it platinum wires connected
by copper wires and binding-
screws with a galvanic battery,
serves to project electrolytic de-
compositions npon the screen.
Perhaps the most beautifdl ap-
pearance is that presented oy th^ crystallucation (^ the metd
from a solution of lead-acetate which is undei^ing electrolysis*.
In order that the cell mav be water-tight, it is necessary that
the india-rubber rings should exert a somewhat powerful com-
f)ression; but even under favourable circumstances slight
eakage is liable to occur in about half an hour after the cell
has been filled ; this, however, would allow ample time for the
display of any of the phenomena above alluded to. Rings cut
from large-sized india-rubber tubing have been found wdl
adapted for the construction of small cells.
X. Notices respecting New Books.
Text'Books of Science. — Principles cf Mechanics. By T. M. GkK)D-
EYE, M.A,j Lecturer on Applied Mechanics at the Bcyal School of
Mines, London : Longmans, Green, and Co. 1874 (small 8vo,
pp. 313).
npHIS book contains an exposition of the principles of mechanics,
•^ such as is commonly given in elementary treatises on that sdenoe.
The exposition is illustrated in two wa,ya— first by means of exam-
ples of the ordinary type, secondly by reference to actual mecha-
nical contrivances mainly of a modem character. There are about
a hundred and eighty illustrations of the former kind ; and of these
about one in every four is taken from the Science Examination
papers drawn up for the annual examinations of the Department
of Science and Art. The second class of illustrations constitutes
the chief peculiarity of the book, and unquestionably its most valu-
able part. The mere names of some of these illustrations will be
enough to show this — e. g, the carrying of com on bands, the feed-
ing of running trains with water, the disintegrating flour-mill, the
ventilation of coal-mines, the lifting of coals, the stone-crushing
machine, Weston's friction coupling, the break-dnun, the crown
valve, the blowing-engine, the hydraulic accumulator, the hydnmlic
crane, &c. These form an assemblage of contrivances which have
never before, to our knowledge at least, been described in any ele-
mentary book ; they render the work before us worthy of the study
of all who are interested in mechanical science ; and we do not
• Mr. W. Crookes, F.R.S., Miggests the electrolysis of solution of thal-
lium sulphate as furnishing a still more beautiful example of crystallization.
Digitized by VjOOQ IC
Notices reipecting New BocJm. 68
Axibt tbiit these iUnslrations alone will csii«e the book to have, as
it undoabtedlj desenres to hare, an extensive oircolatkm.
It wDl be evident from i^e large nnmber of contrivances men-
tioned in ^e above list, that the description of each must be brief,
and that the attention of the reader is mainlj directed to the dj-
namical principles involved in their use. It could scarcely fail to
happen, undw these drcumstanoes, tiiat in some cases p<nnts in
the contrivances are not quite so fully described as the reader
might wish. In others the contrivance is regarded from a p<Hnt of
view which does not bring quite the whc^ subject under notice ;
and tiiis is sometimes a little misleading. For instance, the ooor
trivanee for feeding a running train wi^ water is e<Misidered
simply as an illustration of inertia ; and this probably accounts icft
^ke statement that the water which runs up the tube *' is at rest
ezc^t so far as the movement in a vertical direction is concerned "
(p. 49). As one end of the tube is vertically over the other end, it
is plain that the water before it leaves i^ tube must have acquired
Ihe forward velocity of the train as well as ^ v^tacal velocity
with which it ascends the tube ; and in fact the illustration of thd
inclined plane^ushed beneath the water (p. 49), if properly worked
out, shows this very point : e, g, conceive a particle (P) at rest
* acted on by no forces, and an inclined plane (with an angle c)
moving forward wit^ a velocity Y to come into contact with it ; an
instantaneous action takes place between the plane and the point
alcHig the perpendicular to the plane ; and after Ihe action, P will
move with a uniform velocity aJong a line in space coinciding with
the position of the perpendicular at the instiuit of the action. If
we further suppose that there is no force of restitution, P, while
moving in space along the above-mentioned line, will continue to
touch the plane and appear to run up it. Supposing the mass of
the plane large in comparison with that of P, the horizontal and
vertical components of Ps velocity will be V sin' « and Y sin » cos «.
It is evident from the former expression that, if the plane were
steep, the forward horieontal velocity of P would be nearly equal
to V, and would be quite equal to it if the plane were vertical.
The velocities would be incr^tsed if there were restitution, and the
point would be thrown forward from the plane, of course along the
aforesaid perpendicular. This is true supposing P to be not acted on
by any other force than the momentary action of the plane ; if we
suppose P to be under the action of gravity, the above vdodties
are its horizontal and vertical initial velocities, and the subsequent
motion can be easUy determined on the usual suppositions. Now
the contrivance for feeding running trains with water differs from
the case we have been considering in this — that instead of a mere
inclined plane, a tube with a gradually increasing slope is em-
ployed ; the effect of this is threefold : in th!^ first places the increas-
ing sl<^ makes the action gradual instead of instantaneous, thereby
diminishing the tendency of the instrument to dash the water out
of the trough ; in the neifft place^ if the water, when once in the
tube, have any tendency to fly forward owing to restitution or any
Digitized by VjOOQ IC
64 Notices respecting New Books.
otiier cause, the tendency has no effect so far as the presort qaes«-
tion is concerned ; and, finally, as the tube for a lai^ part of its
.length is nearly or quite rertical, the horizontal velocity of the as-
cending stream cannot fail to acquire the forward velocity of the
train.
The Statement of General Principles and the proofs of particular
theorems contained in the text are (it is almost needless to say so)
correct as far as we have noticed ; and the student who works at
the book conscientiously will doubtless not fail to make it out,
though the style does not generally show in any marked degree tiie
power of clear exposition. There is one point which ought not to
be left unnoticed, as the author lays considerable stress upon it :
he states that he has endeavoured '* above all to show tiiat the re-
lation of the theory of heat to mechanics should be approached by
the student in his earliest inquiries with the same careful thought
with which he will surely regard it when his knowledge and his
powers have become extended and strengthened." And accordingly
the book contains articles in which are explained what is meant by
the mechanical equivalent of heat, by the kinetic theory of gases,
and one or two otner matters. What parts of a subject an author
puts into his book is a matter depending so much on his own judg-
ment as to be rarely the proper subject of criticism ; but we may
perhaps be allowed to record a difference of opinion. It seems to
us, then, that the subject of energy of motion presents difficulties
to the beginner so great that it is best to give him a isxr chance of
becoming familiar with it before introducing him to the far more
difficult subject of Potential Energy, and accordingly that it is better
not to deal with the latter subject in a purely elementary treatise
on mechanics.
EeUpses Past and Future, with Oeneral Hints fcr Observing the Heavens,
By the £ev. S. J. JomrsoH, Parker & Co.: Oxford andLondcm.
1874,
Mr. Johnson, in the work before us, has added considerably to
our prospective knowledge of eclipses, transits, and allied pheno-
mena, and has also given us some interesting information relative
to ancient eclipses, mentioning that the first of which we have a
clear record happened at Nineveh in the year 763 b.c. Noticing in
the order of their sequence the most celebrated eclipses of antiquity,
and bringing up the catalogue of observed eclipses to the present
date, the aumor gives us two interesting chapters (Y. and YI.) : — ^tiie
first on the prospects of the amateur, showing the paucity of large
eclipses in England during the next thirty years ; and the second,
" Curiosities in Lunar Echpses," as bright and black total eclipses,
and those in which both luminaries were above the horizon at the
time of the moon being eclipsed, an obvious effect of refraction.
The first part of the work, m which we have notices of eclipses
from the celebrated one of Ho and Hi 2127 b.c. October 13, to
A j>. 2381 July 21, contains a large amount of information on an in-
teresting branch of astronomy.
Digitized by VjOOQ IC
Royal Society^ G5
From edipsee of the Sun and Moon, the author passes in the
second part of his work to describe prospectirely tiie most interes-
ting planetary phenomena, the periods at which thej may be^ most
adyantageoosly looked for, with the peculiar features they are likely
to present. Allusions are made to the Aurora, Zodiacal light,
Meteors, &c. ; and we notice a remarkable suggestion embodied in a
communication to the ' Spectator ' by the Bey. E. L. Gkui)ett, that
the cities of Sodom and Gk>morrah were destroyed by a group of
tiie meteors following TempeFs telescopic comet of 1866. Mr.
Oarbett giyes six reasons for his suggestion as follows : —
1. From the deduced period of node passage of the comet a
yifiit must haye occurred in the autumn between b.o. 1898 and b.c.
1897, which is fl;enerally assumed as the date of the catastrophe.
2. The earth^ passage of node was on July 31.
3. A yertical tiul of meteors as rain was only possible at sunrise,
the hour of the destruction of the cities.
4. The latitude of the yertical fall agrees with that of the cities.
5. Sodium, the chief element in the deposits formed in the loca-
lity, is the chief element in these meteors as observed by Secchi.
6. Magnesium, which also occurs in the locality, is the only other
ingredient in the meteors conspicuous to Secchi by means of the
spectroscope.
" Suppose," says the writer, " any eyent not due to this comet to
be recorded. The diances against the account presenting these six
agreements with its elements and no disagreements, are three mil*
Hons to one that the history of Sodom is true, and this the phy-
sical cause.**
The work closes with a list of 152 double stars and nebul», ar-
ranged much in the same way as the portion on the Starry Heayens
of Webb's ' Celestial Objects for Common Telescopes,' the angles
ci position of the double stars, as seen near the meridian, being in-
dicated by dots, an addition which we haye no doubt will be duly
i^predated by those readers who are just commencing their obser-
vational career.
XI. Proceedings qf Learned Soeieties.
BOTAL SOCIBTY.
[Continued from toI. zini. p. 457.]
December 11, 1873. — Joseph Dalton Hooker, C.B., President,
in the Chair.
THE following communication was read : —
" On the Action of Heat on Grayitating Masses." By Wil-
liam Orookes, FJEt.S. &c.
The experiments recorded in this paper haye arisen from ob-
senrations made when using the yacuum-balance, described by the
author in his paper "On ttie Atomic Weight of Thallium"*, for
» PbiL Tranf . 1873, toL olriii. p. 277. , "
Phil. Maj. S. 4. V(d. 48. No. 815. Jvly 1874, F
Digitized by VjOOQ IC
66 Royal Society .—Mr. W. Crookes on the
weigfainff Bubetanoes which were of a higher temperature than the
Burroanding air and the weights. There appeared to be a dimimi-
tion of the force of grayitation ; and experiments were instituted
to render the action more sensible, and to eliminate sources of error.
In an historical resume of the state of our knowledge on the sub-
ject oi attraction or repulsion by heat, it is shown that in 1702
the Bev. A. Bennet recorded the fiict that a light substance de-
licately suspended in air was attracted by warm bodies : this he
ascribed to air-currents. When light was focused, by means of a
lens, on one end of a delicately suspended arm, eitiier in air (Mr in
an exhausted receiver, no motion could be perceiyed distinguish-
able from the efEects of heat.
Laplace spoke of the repulsive force of heat. Libri attributed
the movement of a drop of liquid along a wire heated at one end,
to the repulsive force of heat ; but Baden Powell did not succeed
in obtaining evidence of repulsion by heat from this experiment.
Fresnel described an experiment by which concentrated solar
light and heat caused repulsion between one delicately suspended
and one fixed disk. The experiment was tried in air of different
densities ; but contradictory results were obtained under apparently
similar circumstances at different times, and the experiments weto
not proceeded with.
Saigey described experiments which appeared to prove that a
mark^ attraction existed between bodies of different temperaturea.
Forbes, in a discussion and repetition of Trevelyan s experi-
ment, came to the conclusion that there was a repulsive action ex<-
erdsed in the transmission of heat from one body into another
which had a less power of conducting it.
Baden Powell, r^eating Fresners experiment, explained l^a
results otherwise than as due to repulsion by heat. By observing
the descent of the tints of Newton's Bings between glass pliU«s when
heat was applied, Baden Powell showed that the interval between
theplatea increased, and attributed this to a repulsive action of heat^
Faye introduced the hypothesis of a repulsive force of heat to
account for certain astronomical phenomena. He described an
experiment to show that heat produced repulsion in the luminoua
arcjriven by an induction-coil ii^ rarefied air«
l£e author describes numerous forms of apparatus successivelj
more and more delicate, which enabled him to detect and then to
render very sensible an action exerted by heat on gravitating bodies,
which is not due to air-currents or to any other known form of
fwce.
The following experiment with a balance made of a straw beam
with pith-ball masses at the ends enclosed in a glass tube and con-
nectea with a Sprengel pump, may be quoted from the paper : —
<* The whole being fitted up as here shown, and the i^paratus
being full of air to begin with, I passed a spirit-fiame across the
lower part of the tube at 6, observing the movement by a low-power
micrometer; the pith ball (a, h) descended slightly, and then im-
mediately rose to considerably above its originaJ position. It
Digitized by VjOOQ IC
Action of Heat on Gravitating Masses, 67
seemed as if the trae action of the heat was one of attraction, in-
Btantiy oyercome bj ascending currents of air
" 31. In order to apply the heat in a more reguUr manner, a
tii^mometer was inserted in a glass tube, having at its extremity
a glass bulb about 1| inch in diameter ; it was filled with water and
then sealed up. . . The water was kept heated to ,70^ C, the tem-
peratnre of the laboratory being about 15° 0.
^* 32. The barometer being at 767 milUms. and the gauge at zero,
tiie hot bulb was placed beneath the pith ball at h. The ball rose
n^dly ; as soon as equilibrium was restored, I placed the hot-
water bulb above the pith ball at a, when it rose again, more slowly,
however, than when the heat was applied beneath it.
•* 33. The pump was set to work ; and when the gauge was 147
miUims. below the barometer, the experiment was tried again ; the
same result, only more feeble, was obtained. The exhaustion was
continued, stopping the pump from time to time, to observe the
effect of heat, when it was seen that the effect of the hot body
regularly diminished as the rarefaction increased, until when the
gauge was about 12 miUims. below the barometer the action of
the hot body was scarcely noticeable. At 10 millims. below it was
still less ; whilst when there was only a difference of 7 millims. be-
tween the barometer and the gauge, neither the hot-water bulb,
the hot rod, nor the spirit-flame caused the ball to move in an ap-
preciable degree. The inference was almost irresistible that the
rising of the pith was only due to currents of air, and i^at at this
near approach to a vacuum the residual air was too highly rarefied
to have power in its rising to overcome the inertia c^ the straw
beam ana the pith balls. A more delicate instrument would doubt-
less show traces of movement at a still nearer approach to a vacuum ;
but it seemed evident that when the last trace of air had been re-
moved from the tube surrounding the balance — when the balance
WES suspended in empty space only — the pith ball would remain
motionless, wherever the hot body vrere applied to it.
^ 34. I continued exhausting. On next applying heat, the result
showed that I veas hr from having discoveied the law governing
tiliese phenomena; the pith ball rose steadily, and without that
hesitation which had been observed at lower rarefactions. With the
gaoge 3 millims. below the barometer, the ascension of the pith
when a hot body was placed beneath it was equal to what it
had been in air of ordinary density ; whilst with the gauge and
barometer level its upward movements were not only sharper than
they had been in air, but they took place under the influence ci
£nr less heat ; tbe fii^^er, for example, instantly sending the ball up
to its fullest extent.**
A piece of ice produced exactlythe opposite effect to ahotbody.
Numerous experiments are next given to prone that the action
is not dae to efeetridty.
The presence of air having so marked an influence on the action
ol heat, an apparatus was fitted up in whidi the source of heat (a
platinum spiral rendered incandescent by electricity) was inside the
F2
Digitized by VjOOQ IC
68 Royal SocUty .—Mr. W. Crooket on the
Yftouum-tube inatead of outoide it as bef(»e ; and the pith balls ol
the former apparatus were replaced by brass balls. By careful mar
nagement and turning the tube round, the author could place the
equipoised brass pole either over, under, or at the side of the source
of heat. With this apparatus it was intended to ascertain mcHre
about the behaviour of the balance during the progress of the ex-
haustion, both below and above the point of no action, and also to
ascertain the pressure corresponding with this critical point.
After describing many experiments with the ball in various po-
sitions with respect to the incandescent spiral, and at different
pressures, the general result is expressed by the statement that
the tendency in each case was to bring the centre of gravity of the
brass ball as near as possible to the sourbe of h^^t, when air of or-
dinary density, or even highly rarefied air, surrounded the balance.
The author continues : —
*' 44. The pump was then worked until the gauge had risen to
within 5 millims. of the barometric height. On arranging the ball
above the spiral (and making contact with the battery), the attrac-
tion was still 8tr<»ig. drawing the baU downwards a distance of 2
millims. The pump continuing to work, the gauge rosauntil it was
within 1 milHm. of the barometer. The attraction of the hot spiral
for the ball was still evident, drawing it down when placed below
it, and up when placed above it. The movement, however, was
much less decided than before ; and in spite of previous experience
(33, 34) the inference was very strong that i£e attraction would
gradually diminish until the vacuum was absolute, and that then,
and not till then, the neutral point would be reached. Within one
millimetre of a vacuum there appeared to be no room for a change
of sign.
*' 45. The gauge rose until there was only half a millimetre be-
tween it and the barometer. The metallic hammering heard when
the rare&ctioQ is dose upon a vacuum commenced, and the fillip-
ing mercury only occasionally took down a bubble of air. Oa
turning on the battery current, there was the faintest possible
movement of the brass ball (towards the spiral) in the direction ol
attraction.
. " 46. The working of the pump was continued. On next ma-
king contact with the battery, no movement could be detected.
The red-4ot spinJ nmther attracted nor repelled I had arrived at
the critical point. On looking at the gauge I saw it was level with
the barometer.
** 47. The pump was now kept at full work for an hour. The
gauge did not rise perceptibly ; but the metiJlic hammering sound
increased in sharpness, and I could see that a bubble or two ol air had
been carried down. On igniting the spiral, I saw that the critical
point had been passed. The sign had changed, and the action was
mnt but unmistakable repuUum. The pump was still kept going,
and an observation was taken from time to time during several
hours. The repulsion continued to increase. The tubes of the
Digitized by VjOOQ IC
Action of Htat ok QravUating Ma$i€$. 69
pump were now washed oat witii oil of Titriol*, and the working
was ocmtinued for an hoar.
'^ 48. The aeti(m of the incandescent sniral was now |oand to ba
exiesr^UcaIljrq>dlefU, whether it was placed aboTe or below the
brass ball. The finsers exerted a repeUent action, as did also a warm
glass rod, a spirit-lame, and a niece of hot oopper.**
In order to decide once for all whetiier these actions really were
dueto-aar-carrents, a form of apparatas was fitted op which, whilst
it woold settle the qoestion indispatablj, woald at the same time
be likel J to afford information <^ mach interest.
Bj chemical means the author obtained in an apparatus a Tacuam
so neariy perfect that it would not carry a current inm ^ Buhm-^
ko^s coil when connected with platinum wires sealed into the
tube. In such a vacuum the repulsion by heat was still found to
be decided and energetic.
An experiment is next described, in whidi the rays of the sun,
and then ihe di&rent portions of the solar spedrum, are projected
on to the delicately suspended pit^ball balance. In vacuo the
repulsion is so strong as to cause danger to the apparatus, and
resembles that which would be produced by the physical impact of a
material body.
Experiments are next described in which various substances were
used as the gravitating masses. Amongst these are ivory, brass,
pith, platinum, gilt pith, silver, bismuth, selenium, copper, mica
(horisontal and vertioJ), charcoal, Ac.
The behaviour of a glass beam with glass ends in a diemical va-
cuum, and at lower exhaustion, is next accurately examined when
heat is applied in different ways.
On suspending the light index by means of a cocoon fibre in a
kmg glass tube furnished with a bulb at the end, and exhausting
in various ways, the author finds that the attraction to a hot bodv
in air, and the repulsion from a hot body in vacuo are rendered stiu
more apparent.
Speaking of Cavendish's celebrated experiment, the author says
^bat he has experimented for some months on an apparatus of this
kind, and gives the following outline of one of the results he has
obtained : —
<' A heavy metaUic mass, when brought near a delicately sus-
pended light ball, attracts or repels it under the following circum-
stances:—
'' I, WJten ike ball ia in air of ordinary density.
a. If the mass is colder than the ball, it repels the ball.
6. If the mass is hotter than the ball, it aUraets the ball.
** II. When the baU is in a vacuum.
a. If the mass is colder than the ball, it attracts the ball.
h. If the mass is hotter than the ball, it repels the ball."
The author continues: — *' The density of the medium surround-
* This can be effected without interfering with the eihmusiion.
Digitized by VjOOQ IC
70 Royal Sbdeiy : —
ii^ tii0 bttB, the mfttonal of \diich the ball is nuMle, and a Tsty
«l]£ht difference between the temperatures of the mass and tbi
baU, exert so strong an ii^umiee over the attraotiTe and ropulsiYe
force, and it has be^ so difficult for Bie to eliminate all interfeiiDg
actioDs of temperature, eleotrioity, Ac, that I have not yet been
aUe to get distinct evidence of an independent force (not being of
the nature of heat) urging the ball and the mass tqgeUiw.
«* Experiment has, however, showed me that, whilst the action is
in one dhrection in dense air, and in the <^posite direction in a
vacuum, there is an intermediate pressure at whidi differences of
tampeiwture appear to exert little or no interfering action. By
experimenting at this critical pressure, it would seem that such an
action as Was obtained by Cavendish, Beidi, and Baily should be
rendered evideaxt.''
After discussing the explanations which may be given iA these
actions, and i^owing that they cannot be due to auMnirrents, the
author refers to evidences of this repulsive action of heat, and at-
kactive action of cold, in nature. In that portion of Uie sun's
radiation which is called heat, we have the radial repulsive f oroe^
possessing successive propagation, required to explain the phenc^-
mena of comets and the shape and changes of the nebnl». To
compare small things with great-— to argue from pieces of straw up
to heav^ily bodies— it is not improbable that the attraction, now
shown to exist between a cold ana a warm body, vdll equally prevail
when, for the temperature of meltine ice is substituted the cold of
space, f <»r a pith oall a celestial sphere, and for an artificial van
cuum a stellar vmd. In the radiant molecular energy ci. cosmical
masses may at last be found that " agent acting constantlv accord-
ing to certain laws," which Newt<m held to be the cause of gravity.
January 8, 1874, — Joseph Dalton Hooker, G.B., President, in
the Qiair.
The following communication was read : —
" On Electrotorsion.** By G^eo^ge Gore, P.E.S.
This communication contains an account of a new phenomenon
(of rods and wires of iron becoming twisted while under the in-
fluence of electric currents), and a full description of the con-
ditions under which it occurs, the necessary apparatus, and the
methods of using it.
The phenomenon of torsion thus produced is not a microscopic
one, but may be made to exceed in some cases a twist of a quarter
of a circle, the end of a suitable index moving through a space of
80 centimetres (be31 inches). It is always attended by emission
of sound.
The torsipns are produced by the combinea influence of helical
and axial dectric currents, one current passing through a long
copper-wire cml surrounding the bar or wire, and the other, in
an axial direction, through the iron itself. The cause of them is the
combined influence of magnetism in the oidinary longitudinal direc-
Digitized by VjOOQ IC
Mr. 6. Gore on Bk^rot€Tium. 91
tion inAaoed in: liie bar by the ooil-cnrrent, and transterse mag-
netism indueed in it by the axial one.
The torsions are remsibbl j symmetrical, and are as definitely
lebted in dbreclaon to dectric currents as magnetism itself. The
chief law of them is — A current Jhwing from a norih to a 90%Uh
pole produces left-handed toreion, cmd a reveree one rtg7u4uxnded tor^
non (L e. in the direction of an ordinary screw). Although eadbi
eorrmt ahme will produce its own magnetic effect, sound, and in-
ternal molecular morement, neither al<me will twist the bar, unless
the bar has been preyiously maenetised by the other. Suceessiye
coil-eurrents alone in opposite oirections will not produce torsion,
neither will suceessiye and opposite axial ones.
Hie torsions are influenced by previous mechanical twist in the
iron, by mechanical tension, and by terrestrial magnetic induction.
The direction of them depends both upon that of the axial and of the
oofl-currents, but appears to be determined most by the former. A
few cases occur in which the currents, instead of developing torsion,
produce detorsion ; but only two instances, out of many hundreds,
have been met with in which torsion was produced in a direction
opposite to that required by the law.
Bingle torsions vary in magnitude from 0*5 mUlim. to nearly 30
millims. of movement of the end of an index 47 centimetres long ;
the smaller ones occur when the two currents are transmitted
alternately, and the large ones when they are passed simultane-
ously ; the former generally leave the bar in a twisted state, the
latter do not. Those produced by axial currents succeeding coil
ones are nearly always much larger than those yielded by ooU-cur-
rents succeeding axiiu ones, because the residual magnetism left by
ttie coil-current is the strongest. The order of succession of ihe
currents affects the torsions in all cases, altering their magnitudes,
and in some few instances even their directions. In steel all the
torsional effects are modified by the mechanical and magnetic
properties of that substance.
Each current leaves a residuary magnetic effect in the bar,
amounting in iron to about one tenth of its original influence. The
residuary magnetism of coil-currents is affected and sometimes re-
versed by axial ones ; and that of axial currents is also removed by
coil ones, and by a red heat. The condition left by an axial current
is smaller in degree and less stable, in a vertical iron wire or one in
the terrestrial magnetic meridian, than that left by a coil one, partly
because of the influence of terrestrial magnetism ; but in a position
at right angles to that the effect is different.
The torsion produced by a coil-current may be used as a test,
imd partly as a measure, of the residuary effect of an axial one ;
and that produced by an axial currrait may be employed to detect,
and to some extent measure, ordinary magnetism in the bar. As
an opposite coil-current at once reverses the ordinary longitudinal
magnetism of a bar of iron, so also an opposite axial one at once
reverses its transverse magnetism.
Many instances have been met with in which the transverse and
Digitized by VjOOQ IC
78 Oeoloffical Society : —
kmfltudiBal magnetic stateB produced bj the two currraits coen-
istea in the same substance. The tinrsional influence of the ex-
cited heHz is distributed equally throughout its l^agth ; so also is
that of the current in the bar. AU the torsions are doselj reUted
to the well-known electric sounds, and to particular positions and
internal moyements of the particles of the iron.
Signs of electrotorsion were obtained with a bar of nickel, bat
not with wires of pUitinum, silver, copper, lead, tin, cadmium,
sine, magnesium, aluminium, brass, or German-silTer, nor with
a tldak rod of sine, or a cord of gutta percha.
eEOLOOICAL 80CIBTY.
[Continiied from toI. zlvii. p. 462.]
June 25, 1873.— Joseph Frestwich, Esq., F.B.S., Yice-Preeident,
in the Chair.
' The following communications were read : —
1. '* On six Lake-basins in Argyllshire." By His Grace the Duke
of Argyll, K.T., F.R.S., President
The author referred to the part ascribed to glacial action in the
formation of lake-basins, and described the basins of six lakes in Ar-
gyllshire, the characters presented by which seemed to him incon-
sistent with their having been excayated by ice. Among these lakes
were Loch Fyne, Loch Awe, Loch Leokan, and the Dhu Loch. The
upper part of Loch Fyne was said to be out off fh>m the rest by a bar
of islands, with only one or two deeper passages. The country about
Loch Fyne was described as consistiog of Upper and Lower l^urian
mica-slates, which have been violently contorted, their normal strike
being indicated by the direction of the valleys. Loch Fyne occupies
a niche in the slope of the rocks, having an escarpment on one side
and the shelving strata on the other, ^e existence of a fault along
the line of the loch was probable, but could not easily be ascertained.
Its greatest depth in this part was said to be 84 fathoms. Its
banks show marks of glaciation, whereon the sur&oe is well adapted
for their preservation ; the strongest marks are on those rock-faces
which look up the loch. Between Loch Fyne and Loch Awe the
mica-slates are interstratified with granite, which the author be-
lieved to have been forced up between the plains of stratification by
the pressure caused by the falling in of the mica-slates, as frag-
ments of the latter rock are imbedded in the granite. The author
described the different structure of the two banks of Loch Awe, the
upper part of which seemed to him to lie in a synclinal trough ; and
its waters were only prevented by a low col from finding their way
to the Atlantic in this direction, instead of from the lower end.
The formation of the basin of Loch Awe seemed to the author to be
due solely to geological structure, as vras also the case with another
lake beyond the head of Loch Awe. The surrounding country was
said to be full of smaller lake-basins, the formation of which might
be due to the denudation of the softer mica- schists lying below the
Digitized by VjOOQ IC
Prof. R. Owtn on the SkuU of a dentigerous Bird. 78
gnmite ridges. But in some cases the basins were excavated in the
latter; Loch Leckan was mentioned as an example. It is about a mile
long, from 100 to 200 yards broad, and no less than 18 Ifiathoms deep.
At the top of its southern bank, which consists of granite, there is
another lake (Loch-nar-Craig), about 200 yards broad and 9 fathoms
deep. The surrounding hUls are low, and there appeared to be no
source which could furnish ice to'excavate a lake of such depth as Loch
Leckan ; and further, the author contended that if one of these two
basins had been excavated by ice, the other could hardly have been
preserved intact. Two other lakes, excavated on the summits of
granite ridges, were mentioned; and the author could not conceive
how either a glacier or an ice-cap could have produced such basins.
The Dhu Loch, separated from Loch Fyne by a bank of gravel about
a mile broad, is entirely in detrital matter, which the auUior thought
might have been accumulated in its present form by the sea beating
against the end of a glacier. From its position and level, the Dhu
Loch rises and falls with the tide; and it would appear that it
formerly extended some miles furUier up the valley, where the
author had found days containing a mixture of marine and fresh-
water DiatomacesB. In five of these cases the author thought it was
impossible that the basins are due to glacial action.
2. <' Description of the Skull of a dentigerous Bird {Odantopteryx
uHiapiais, Owen), from the London Clay of Sheppey." By Prof.
Kichard Owen, F.R.S., F.G.S.
The specimen described by the author consisted of the brain-case,
with the basal portion of both jaws. The author described in detail
the structure and relations of tiie various bones composing this skull,
which is rendered especially remarkable by the denticulation of the
alveolar margins of the jaws, to which its generic appellation refers.
The denticulations, which are intrinsic parts of the bone bearing
them, are of two sizes, — ^the smaller ones about half a line in length,
the larger ones from two to three lines. The latter are separated
by intervals of about half an inch, each of which is occupied by
several of the smaller denticles. All the denticles are of a triangular
or compressed conical form, the larger ones resembling lania-
riee. Sections of the denticles show under the microscope the un-
mistakable characters of avian bone. The length of the skull be-
hind the fronto-nasal suture is 2 inches 5 lines ; and from the pro-
portions of the frtigment of the upper mandible preserved, the author
concluded that the total length of the perfect skull could not be less
than between 5 and 6 inches. The author proceeded to compare
the fossil, which he declared to present strictly avian characters,
with those groups of birds in whidi the beak is longer than the true
cranium, a character which occurs as a rule in the Aves aquaiiecB,
He stated that none of the Waders have the nostrils so remote from
the orbits as in Odoniopteryx ; and this character, with the absence
of the superorbital gland-pit, limits the comparison to the Totipal-
mates and Lamellirostrals. The former are excluded by their not
having the orbit bounded by a hind wall as in OdontopUryx ; and in
this and other peculiarities the fossil seems to approach most nearly
Digitized by VjOOQ IC
74 Geotogical Sociefy: —
to the Attatid», in the aear alUeB of which, the Gkweanden and Mer-
gansers, the beak is fonushed with strong pointed denticnlations.
In these, however, the tooth-like processes bdong to the homy bill
only ; and the author stated that the production of die alveolar margin
into bony teeth is peculiar, so fiur as he knows, to Odnntopteryx,
He condiuded, finom the consideration of all its characters, '' that
Odontopteryx was a warm-blooded, feathered bqied, with wings ;
and further, that it was web-footed and a fish-eater, and that in the
catching of its slii^>ery prey it was assisted by this pterosanroid
armature of its jaws." In oondusion, the author indicated the dia-
factors separating Odawtopteryx from the Cretaceous fossil sknll
lately described by Prof. 0. G. Manh, and which he affirms to have
small, similar teeth implanted in distinct sockets.
3. " Contribution to the Anatomy of Hypsihphodon fbxii, an
Account of some recently acquired Remains of this Dinosaur." By
J. W. Hulke, Esq., F.R.8., F.G.8.
After referring to Professors Owen and Huxley's descriptions of
the Mantell-Bowerbank skeleton in the British Museum, and to tiie
paper by the last-named gentleman on the skull of this Dinosaur
read at a meeting of this Society in 1 870, the author communicated
details of its dentition, the form of its mandible, and that of the
cones of the shoulder and fore limb, and of the haunch and hind
limb, hitherto imperfectly or quite unknown. The resemblance to
Igwmodon is greater than had been supposed ; but the generic di-
stinctness of HypsUcjphodon holds good.
4. << On the Glacial Phenomena of the ' Long Mand,' or Outer He-
brides." By James Geikie, Esq., F.R.S.E., F.GJ3., of H.M. Geolo-
gical Survey of Scotland. — First piqper.
The author commenced by describing the physical features of
Lewis, which he stated to be broken and mountainous in the south,
whilst the north might be described as a great peat moss rising
gradually to a height of about 400 feet, but with the rock breaking
through here and there, and sometimes reaching a higher elevation.
The north-east and north-west coasts are comparatively unbroken ;
but south of Aird Laimisheadar in the west and Stomoway in the
east, many inlets run far into the country. The island contains a
great number of lakes of various sizes, which are most abundant in
the southern mountain tract and in the undulating ground at its
base. The greater part of Lewis consists of gneiss, the only other
rocks met with being granite and red sandstone, and conglomerate
of Cambrian age. The stratification of the gneissic rocks is generally
well-marked ; the prevalent strike is N.E. and 8.W., with S.E. dip,
generally at a high angle. The author described in considerable
detail the traces of glaciation observed in the lower northern part of
Lewis, and inferred from his observations that the ice passed from
sea to sea across the whole breadth of this district, and that it not
only did not come from the mountainous tract to the south, but must
have been of sufficient thickness to keep on its course towards the
north-west undisturbed by the pressure of the glacier masses which
must at the same time have filled the glens and valleys of that
Digitized by VjOOQ IC
Mr» Campbell on the Okdal Phenomena of the Hebrides. 76
nMmQteb^egion. After deeoribing the ohareoten prsBented by the
bottom-till in the northern part ^ Lewis, the antiior proceeded to
notice those of the lakes, wane of whieh toend nortii-weet and south-
east, others north-east and sonth-west, irfailsl those <^ the mountain
district follow no particolar direction. The lake-basins of the first
seiies he regarded as fonned at the same time and by the same
agency as the roehee mouionnies and other marks of glacial action ;
jthey are tme rock-basins or hollows between paiallel banks formed
whoJly of till, or of till and rock. The N JB. and S.W. lakes coin-
cide in direetion precisely with the strike of the gneiss ; and the
anyior explained their origin by the deposition of till by the land-ice
in passing over the escaipments of tiie gneiss facing the nortii-west.
Hie lakes of the mountain district are regarded by the author as all
prodneed by glacial erosion. The auth^ considered ^t the ice
which passed over the northern part of Lewis could only have come
from tiie mainland. Beferring to the glaciation of Eaasay, he
showed that the ice-sheet which effected it must have had in the
Jnner Sound a deftth of at least 2700 feet ; and taking this as ap-
proximately Uie thickness of the mer de glace which flowed into the
Minch, which is only between 50 and 60 fathoms in depth, no part
of this ice could have floated, and the mass must have pressed on
over the sea-bottom just as if it had been a land suiiiace. Lse
coming from Butherland must have {urevented the flow of the Boss-
shire ice through the Minch into the North Atlantic, and forced it
over the low northern part of Lewis ; and the height to which Lewis
has been glaciated seems to show that the great ioe^heet continued
its progress until it reached the edge of the 100-fathom plateau, 40
or 50 miles beyond the Outer Hebrides, and then gave off its ice-
bergs in the deep waters of the Atlantic.
5. *' Notes on the Glacial Phenomena of the Hebrides." By J.
F. Campbell, Esq., F.G.S.
This communication consisted of notes extracted from the author's
journal, giviog his observations of indications of glacial action in
various idands of the group of the Hebrides. Heynish in Tiree is
500 feet high, and has many large perched blocks on its top. These
blocks are <^ gneiss ; and the author thought they came from the
north-west The Barra islands are described as rocky, and resem-
bling the hill-tops of a submerged land. All ice-marks found by the
author seemed to him to come from t^e north and west. He thought
that the final grinding was given by floating ice when the land was
more submerged than at present. At Castle Bay, in Barra, the au-
thor observed well-preserved glacial strise at the sea-level in a direc-
tion from N.N.W. The whole island is glaciated and strewn with
perched blocks. Glacial indications were also observed in South Uist,
B^ibecula, and Skye ; and the aitthor stated that, on the whole, he
was inclined to think that the last glacial period was marine, and
that heavy ice came in from the ocean, the local conditions being
like those of Labrador. The author regarded most of the l^e-
basins of the Hebrides as formed by ice-action, and considered that
the ice by which those islands were glaciated came from Greenland.
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76 Geological SocUly.
6. *' On Fossil Corals from the Eocene Formation of the West
Indies." By Prof. P. Martin Duncan, M.B., F.R.S., V.P.G.8.
The author had considered his lahours amongst the fossil corals of
the West-Indian Islands finished ; hut lately a yery fine collection has
heen sent to him from the Unirersity of Upsala, and Mr. P. T. Clere
of Stockholm. The specimens were collected from limestone and coral
conglomerates, which are covered by and rest upon ydoanic d^ris
and ejectamenta in the Island of St. Bartholomew. The species re-
presented there are numerous, and may he divided into :— ^roup 1,
species not hitherto known ; 2, species with a Cretaceous fades ;
3, species characteristic of the horizons of the Upper Eocene and
Oligocene deposits of Europe ; 4, species found also in the Nummu-
Utic deposits of Europe and Sinde; 5, species belonging to the
recent coral fauna ; 6, species belonging to genera which belong to
the Jurassic fauna, and to the Caribbean.
The determination of the forms of the associated MoUusca and
Echinodermata permit the following deposits being placed on a
general geologic^ horizon — the limestone and conglomerate of St
Bartholomew, the dark shales beneath the Miocene of Jamaica,
the beds of San Fernando, Trinidad. These were probably contem-
poraneous with the Java deposits, the Eocene of the Hala chain,
the great reefs of the Castel Gomberto district, the reefs of Ober*
berg in Steiermark, and the Oligocene of Western Europe.
The author has already described reef corals from the Lower Cre*
taceous (Upper Greensand) of Jamaica ; and the size of the sped*
mens proves that the reef was exposed to the surf of an open sea.
To these reefis succeeded on the same area others in the Eocene
time, in the Miocene and Pliocene ; and there are modem reefis in
the neighbourhood.
The affinities and identities of the fossil forms with those of con-
temporaneous reefs in Asia and Europe, and the limitation of the
spedes of the existing Caribbean coral fauna, point out the correct-
ness of the views put forth by 8. P. Woodward, Carrick Moore, and
the author, concerning the upheaval of the Isthmus of Panama after
the termination of the Miocene period.
7. " Note on the Lignite-deposit of Lal-Lal, Victoria, Australia.''
By R. Etheridge, Esq., Jun., F.G.S.
The author described this depodt, which is worked at the village
of Lal-Lal, south of Mount Bunniyong. A boring towards the centre
of the deposit showed about 73 feet of sand, day, and gravel, 3 feet
of fireday, and 1 15 feet of lignite. The lignite is an earthy bitu-
minous coal, composed of branches, roots, &c. of coniferous trees.
In the mass there are a few thin seams of jet and day-beds, accom-
panied by two kinds of resin. The lignite is very poor in carbon.
It is almost entirely composed of remains of coniferous plants not
now existing in Victoria ; and the author conddered that it is nearly
of the same age as the Lignite depodt of Morrison's Diggings, whidi
has been regarded as Miocene.
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C 77 ]
XII. IntelUgenee and Migcellaneau$ Articles.
ON THB FLOW OF SALINE SOLUTIONS THROUGH CAPILLARY TUBB8.
BT THEODORE HUBfiNER.
rPHE velocity of the flow of solutions in capillary tubes appears
^ not to depend solely on their weight and capillary adhesion.
Poiseuille has demonstrated that the velocity of flow of a mixture of
water and alcohol decreases in proportion as the specific gravity
increases by the addition of larger and larger quantities of water,
to a Tninimiim which corresponcis exactly to the maTiTnum of con-
traction of the mixture. GKrard found that the velocity of flow of
chloride of sodium is less than than that of a solution of chloride
of potassium of the same density.
M. Hiibener thought that, beside the adhesion and the weight of
the liquid, an important factor for the velocity of flow of a solution
must be the intermolecular friction resulting from its greater or
less cohesion ; and to test this he has compared the velocities of a
nomber of solutions of very different chemical compositions brought
to the same density.
The liquid was introduced into a vertical rectilinear glass tube of
50 centims. length and 1*78 centim. diameter, having a capillary
continuation of about 40 centims. length. The large tube presented
two marks; and with a seconds-watch the time was accurately
measured which was required for the level of the liquid to tall from
one of these marks to the other.
Operating in this way upon solutions of chloride, bromide, and
iodiae of potassium, of chloride of sodium and of ammonium, with
a density of 1*059 and at a fixed temperature, the author ascertained
tiiat the velocity of flow of saline solutions is as much lower as the
atomic weight of the salt dissolved is less. For the different binary
bodies abovein£cated, it is the metal which has the greatest influence
opon the velocity of flow, much more than the metalloid. The va-
riations presented by the velocity from one body to another are as
much more marked as the tube is more capiUary and as the con-
centration of the solution is greater.
On comparing two solutions, of chloride of sodium and potassium,
at 1*1058 density, the author arrived at the remarkable result that
the times of flow of these two salts are found to be very sensibly
proportional to their equivalents. From this experiment, and from
others fuialogous, extended also to the chlorides of the alkaline-eiarthy
metals barium, strontium, magnesium, M. Hiibener thinks it may be
concluded generally with a high degree of probability, that the velo-
cities of flow of these bodies in solution in. water, to a certain degree of
concentration, are in the same ratio as their equivalents.
The explanation of these facts is, according to M. Hiibener,
to be found in the circumstance that the molecules of substances
which have a higher equivalent are larger, but, on the other hand,
in less number, and consequently must give rise to less friction
with the solvent in which they ai*e held, thus communicating greater
Digitized by VjOOQ IC
78 IrUeUigenee and Miseellaneoui Articki.
mobility to the solution. — BihUaiheque UniverBsUe, AreMvu dtt
Sciences Phys. et Nat. No. 197, pp. 76, 76.
BY W. LOWEET.
In performing Melde'e experiment upon the vibrations of
strings, it is desirable to change the tension of the vibrating cord
in a continuous manner. The ordinary method of attaching
weights to the cord does not admit of this with precision ; and with
small weights the movement of the weight itself, on account of the
rapid vibration of the string, prevents the formation of the ventral
segments with regularity. I have adopted the following method : —
A glass tube graduated into millimetres is weighted so as to float
in a vertical position: this is attached to the silk cord whidi
hangs from the prong of the tuning-fork, and is placed in a glass
vessel filled with water. This latter vessel is provided with a
siphon, by means of which the water can be drawn ofF at pleasure.
It will be readily seen that, by drawing off the water from the
larger vessel, the displacement produced by the graduated glass
tube is diminished, ana the tension of the string thereby is increased.
By diminishing or increasing the amount of water in the larger
vessel the tension can be diminished or increased to the desirod
extent.
In order to make quantitative experiments, the tube is in the first
place connected with the arm of a delicate hydrostatic balance.
The balance is adjusted when the level of the water in which the
tube floats is at the zero of the millimetre scale. In order to
avoid errors in reading, it is best to use a cathetometer. The
weights which are necessary to keep the index of the balance at
aero, when the level of the water in the outer vessel falls through
the millimetre divisions on the graduated tube, are noted, llie
upward pressure of the water, and consequently the tension upon
the suspending cord, are then given in grams.
In order to show the regiuarity of the method, the following
results of one experiment are given. In the experiments, a glass
tube which, immersed at 110 millims. on the scale, weighed two
grams gave, when the level of the water in the outer vessel was
lowered, the following : —
Immersed at 110 millims. Weight « 2 grams.
102 „ „ 2-5 „
tf 93'5 „ „ 3 „
„ S5 ^ „ „ 3*6 „
»> 76-5 „ „ 4 „
„ 67*6 „ „ 4*5 „
»» ®0 „ „ 6 „
ff 43 „ „ 6-6 „
In these experiments a fidl *of 8*1 millims. corresponded to a
difference of *5 of a gram. It is evident by increasing the sise of
the outer vessel that a large amount of water would measure a
slight displacement. When the cord was set in vibration, the fol-
lowing results were obtained : —
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TntelUgenee and Miscettaneaus Articles. 79
Paint Wmgfate
of immenion. in grams. yibrations.
110 2 6
84 3-5 6
76 4 4
30 6-7 3
The ratio of the numbers in the second and third columns will be
found to follow Melde's law.
For qualitative or quantitative experiments upon beats or Lissa-
jous curves this method of loading the prong of a tuning-fork can
advantageously replace the bit of wax or the sliding weight, since
we have at our command a quick and precise method of adjustment.
— Silliman's American Joumaly May 1874.
ON CONSTANT ELECTRIC CURRENTS. BY M. HEINE^ OP HALLE.
Kirchhoff* has developed a simple expression for the elebtric
Potential, with a constant current, in every point P of a circular
omogeneous plate into which the current enters at given points
Aj, A^, If each letter E represents a constant depending on
the strength of the current entering at the point A„ and if B^ is
the conjugate point to A^, the electric potential of the circle in the
point P becomes
V=2E,log(PA,.PBJ, (a)
when the summation is extended to all the points of inflow. Two
points A, B of the circle are called conjugate which lie on the same
right line M AB starting from the centre M, if the radius forms the
mean proportional between MA and MB.
I have found the expression of the potential also for plates of
other shapes, and will here give it for the ellipse and the rectangle.
Let the excentridty of the ellipse be 1 ; let the fourth power of
ihe difference of the semiaxes (oi which the greater represents the
axis of the real, the smaller that of the imaginary) be put =sq.
Let each point z of the ellipse be described by the elliptic function
/2K . \
$nl — arc sin z j,
therefore the entire ellipse upon a circle with the radius -j^ (as M.
Sdiwarz has shown). If now a, p are the images of the inflow-
points A and an arbitrary point P of the ellipse, and if h denotes
the point in the circle of radius —t=. conjugate to a, the electric po-
tential of the ellipse in the point P will be
V«SE'log(pa..i>5j (/3)
If, lastly, we have a rectangle OXNY, whose base OX has the
leneth w and is the axis of the real, and its height OY equals
— log ^ and is the axis of the imaffinary, we construct for each
point ot inflow A the three reflected images B, G, D which arise
when A is assumed to be luminous, OX and OY reflecting (^-l:y»,
«— y», — ^— y», — ^-fy*)* I^ ^^^ ®*<5h point z be represented by
♦ Pogg. Aim. vol. Ixiv. p. 497, v<^. Ixvit. p. 344.
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80 Intelligence and Miicellaneoui Art%ele$.
«n* — , and thereby A, B, C, D, and the arbitrary point P of the
IT
rectangle fall upon points a, 5, c^ d, p, the electric potential of the
rectangle in the point P is
V=5 E, log (pa, .pb, .pc, .pd,). (y)
Quincke* bases his experiments, on the potential in very large
square plates when the points of inflow are in the diagonal, upon
a formiila of approximation which in our notation would be
V=? E, log (PA, . PB, . PC, . PDJ.
It is now apparent, if this be compared with the exact formula (y\
that it results from the latter, if $nz may be supposed propor-
tional to z, therefore with very large rectangular plates — or, betttf ,
under the supposition that P and the A's lie near an angular
point of the rectangle. The approximation-formula therefore holds
also when the rectangle is not a square and when the inflow-points
do not lie on the diagonal.
The derivation of these expressions I intend to communicate, in
a connected form, to Borchardt's Journal fur Mathematik. For
this reason I omit here the exhibition in a purely analytical form,
without the aid of geometry, of the relations expressed by (/3) and
(y). — Monatsherieht der honiglich preussischen Akademie der Wia-
senseh, zu Berlin, March 6, 1874.
ON THE NATUEE OF THE ACTION OP LIGHT UPON SILVER BRO-
MIDE. BT H. CAREY LEA, PHILADELPHIA.
When silver bromide is exposed for a moment to light, it under-
goes no visible change, but has acquired the property of passing to
an intense black when treated with p3rrogallic add and an alkaU.
As to the nature of this black substance, there has existed con-
siderable diversity of opinion. In a paper published on the subject
about a year since by Captain Abney, F.C.S., he expressed the
opinion that it was an oxide of silver.
Some years since, while investigating the action of light upon
silver iodide, I succeeded in provins; that the black substuice
which is produced when silver iodide is exposed to light in presence
of silver nitrate contains iodine, and is therefore either a sub-
iodide or an oxy-iodide. The quantity obtained was too small to
enable me to ascertain which. When this black substance was
treated with nitric acid, normal yellow silver iodide was left behind,
and silver was found on solution.
I have recently applied the same treatment to the bromine com-
poimd with similar results. I And that when silver bromide is
treated with pyrogallic acid and alkali after exposure to light, the
black substance which remains contains bromine, and is resolved by
nitric add into normal silver bromide (left behind as a pale yellow
film) and silver, which passes into solution. It is therefore either
a subbromide or an oxy-oromide, not an oxide, probably the former.
The existence of these compounds is evidently an argument for
doubling the atomic weight of lUver, as has recently been proposed
on other grounds. — SilHman's Am&riean Journal^ May 1874.
* Pogg. Ann, vol. xcvii. p. 382.
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I'
I
4
1^
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THE
LONDON, EDINBURGH, and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE,
[FOURTH SERIES.]
AUGUST 1874.
XIII. On Attraction and Repulsion accompanyirw Radiation^
By William Crookes, F.U.S. ^c.*^
[With a Plate.]
BEFORE describing the apparatus and experiments which
illustrate the attraction and repulsion accompanying ra-
diation^ it will perhaps be best to draw attention to the modifi-
cation of the Sprengel pump which has so materially assisted
me in this investigation.
Fig. 1 (Plate I.) shows the pump as now in use. Working
so much with this instrument^ I have endeavoured to avoid the
inconveniences attending the usual mode of raising mercury
from the lower to the upper reservoir. The mercuiy is con-
tained in a closed glass reservoir A^ perforated with a fine hole
at the top. This reservoir is attached to a block capable of free
movement in a vertical line and running in grooves, and con^
nected with the lower resei*voir by a flexible tube g. This tubing
is specially made to stand a considerable pressure of mercury.
It consists of a double thickness of india-rubber tubing enclosing
a canvas tube in the centre, the whole being vulcanized together.
When the whole of the mercury has run through the pump,
the reservoir and slide can be lowered by liberating a detent, T,
and letting it descend to the block L. H is a glass reservoir
which receives the mercury after flowing through the pump.
When the reservoir A is emptied and has been lowered to the
block L, the mercury from H is admitted into A by opening
ihe tap I. At/ is another tap, of platinum, to regulate the flow
of mercury through the pump, c, c, d are mercury joints, it
* A Lecture delivered before the Physical Society, June 20, 1874. Com-
municated by the Societv.
Phil. Mag. S. 4. Vol. 48. No. Z\Q. Aug. 1874. G
Digitized by VjOOQ IC
82 Mr, W. Crooke« on Attraclion and
being inconvenient to have the apparatus in one piece of tubing,
and not always possible to seal the different portions together
by fusion. « « is a barometer dipping into the same vessel as
the gauge-barometer P> the two thus forming a differential
system by which the rarity of the atmosphere in the apparatus
undergoing exhaustion can be easily estimated, dd is a milli-
metre-scale with pointed end, attached to the gauge and capable
of being raised or lowered so as to make the point just touch
the surface of the mercury, i is a reservoir of strong sulphuric
acid, exposing as much surface as possible, but allowing the air
to pass across it without resistance. The mercury joint (f may
either be closed with a piece of glass rod ground in, or it may have
either of the two pieces of apparatus t and k fitted to it. A is a
mercurial siphon gauge, which is useful for measuring very high
rarefactions in experiments where difference of pressure equal
to a tenth of a millimetre of mercury is impoitant. t is for still
higher rarefactions ; it is simply a small tube having platinum
wires sealed in, and intended to be attached to an induction-
coil. At exhaustions beyond the capabilities of the mercurial
gauge I can still get valuable indications of the nearness to a
perfect vacuum by the resistance of this tube. I have frequentlv
carried exhaustion to such a point that an induction-spark will
not strike across the small distance {\ inch) separating the wires
of the vacuum-tube, h is the mercury-tap usually employed for
letting air into the apparatus, and also for moistening the inte-
rior of the pump with oil of vitriol. / is a spiral of glass for
attaching the various pieces of apparatus requiring exhaustion.
As blown or fused joints are indispensable, this form of con-
necting piece is adopted to ensure the necessary flexibility,
m is a trap to catch any air which might leak in through the
platinum tap/, or the various joints in the lower part of the
tubing g.
The reservoir A being filled with mercury, the tap I is turned
off and the reservoir is raised to the top of the slide where it is
supported by the detent T. On opening the tap /the mercury
rises in the tube /A, and, falling through the chamber N, carries
with it the air contained in the tube R, and in the apparatus
attached to the tube /, as in the ordinarv Sprengel pump. At N
the tubing is enlarged in order that the mercury may not be
forced up the tube R, as otherwise frequently happens if the
tubes or the mercurv gets soiled.
J, J are iron brackets supporting tie apparatus. S is a large
inverted glass receiver, to collect the small portions of mercury
which are unavoidably and constantly being spilled; it should
contain a little weak alkaline solution.
The part of the tubing g,f, A, N forms a barometric siphon
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Repulsion accompanying Radiation. 88
arrBBgement, which effectually prevenU air getting into the
pump from the reservoir A when the mercury has comphjtely
run out. In this case no harm whatever is done to the opera-
tion : the vacuum is not injured ; and the exhaustion proceeds
immediately on retransferring the mercury from the reservoir H
to the reservoir A^ and raising A again into its place. The ap-
paratus, as thus aiTsnged^ is readily manageable with certainty
of obtaining a barometric vacuum.
The mercury fall-tube of a pump in constant use frequently
wants cleaning. I find the most effectual means of doing this
is to put oil of vitriol into the funnel h, and then^ by slightly
loosening the glass stopper^ allow a little of the strong acid to
be carried down the tube with the mercaiy. With care this
can be effected without interfering with the progress of eihaus«>
tion. The residual acid adhering to the walls of the chamber
N does good rather than harm. When sufficient sulpbnrio acid
has run into the fall-tube, the funnel-stopper can be. perfectly
closed by pressing it in with a slight twist and then filling up
with mercury.
Many physicists have worked on the subject of attraction and
repulsion by heat. In 1792 the Bev. A. Bennet recorded the fact
that a light substance delicately suspended in air was attracted
by warm bodies; this he ascribed to air-currents. When^ by
means of a lens, light was focused on one end of a delicately sus-
pended arm, either in air or in an exhausted receiver, no motion
could be perceived distinguishable from the effects of heat.
After Mr. Bennet the subject has been more or less noticed
by Laplace, libri, Fresnel, Saigey, Forbes, Baden Powell, and
Faye ; but the results have been unsatisfactory and contradictory.
My first experiments were performed with apparatus made on
the principle of the balance. An exceedingly fine and light arm
is delicately suspended in a glass tube by a double-pointed
needle ; and at the ends are affixed balls of various materials.
Amongst the substances thus experimented on I may mention
pith, glass, charcoal, wood, ivory, cork, selenium, platinum,
silver, aluminium, magnesium, and various other metals. The
beam is usually either of glass or straw.
The apparatus, consisting of a straw beam and pith-ball endS|
being fitted up as here shown attached to the pump, and the
whole being full of air to begin with, I pass a spirit-lamp across
the upper part of the tube just over one of the pith-balls. The
ball rises. The same effect is produced when a bulb of hot water,
or even the warm finger is placed over the pith-ball.
On working the pump and repeating the experiment, the
attraction to the hot body gets less and less, until it becomes nily
and after a certain barometric pressure is passed, the attractiou
G2
Digitized by VjOOQ IC
81 Mr. W. Crookea on Attraction and
gives place to repulsion^ which gets stronger and stronger as the
vacuam approaches perfection.
In order to illustrate more strikingly the influence exerted by
a trace of residual air, an apparatus (fig. 2) is here shown in
which the source of heat (a platinum spiral, a, rendered incan-
descent by electricity) is inside the glass tube instead of out-
side it as before. A mass of magnesium, i, turned conical, is
suspended in a glass tube, c J«, by a fine platinum wire of such
a length as to vibrate seconds. The upper end of the platinum
wire is sealed into the glass at «, and passes through to the out^de
for the purpose of electrical experiments. The platinum spiral
is arranged so that when the pendulum hangs free the magne-
sium mass is about \ inch from it. In air the red-hot spiral
produces decided attraction on the magnesium ; and by properly
timing the contacts with the battery, a considerable swing can
be acci^mulated. On perfectly exhausting the apparatus, how-
ever, tha^ incandescent spiral is found to energetically repel,
and a very few contacts and breaks properly timed are suffi-
cient to get up the full swing the pendulum is capable of.
A siiMpler form of the apparatus for exhibiting the phenomena
of attraction in air and repulsion in a vacuum consists of a long
glass tube a b (fig. 8) with a globe c at one end. A light index
of glass with pith-balls at the ends d^ e is suspended in this globe
by means of a cocoon fibre. When the apparatus is full of air
at ordinary pressure, a ray of heat or light falling on one of the
pith-balls gives a movement indicating attraction.
When the apparatus is exhausted until the barometric gauge
shows a depression of 12 millims. below the barometer, neither
attraction nor repukion results when radiant light or heat falls
on the pith. When the vacuum is as good as the pump will
produce, strong repulsion is shown when radiation is allowed to
fall on one end of the index. The heat of the hand, or even of
the body several feet ofl^, is quite sufficient. The action is in
proportion to the surface acted on rather than to the mass.
The barometric position of the neutral point dividing attrac*
tion from repulsion varies with the density of the mass on which
radiation falls, on the ratio of its mass to its surface, and in a
less degree on the intensity of radiation. In the case of pith it
is seen to lie at about 12 millims. below a barometric vacuum,
whilst with a heavy metal it is within a tenth of a millim. of a
vacuum. Experiments to try to determine the law governing
the position of the neutral point are now in progress.
Ice, or a cold substance, produces the opposite effects to heat.
Thus a bar of pith suspended in a vacuum is energetically re-
pelled by the warm hand, whilst it is as strongly attracted by a
piece of ice. Cold being simply negative heat^ it is not easy at
Digitized by VjOOQ IC
Repulsion accompanying Radiation. 85
first sigbt to understand how it can produce attraction. The
law of exchanges, however, explains this perfectly. The pith
index and the whole of the surrounding bodies are incessantly
exchanging heat-ra^s ; and under ordinary circumstances the
income and expenditure of heat are in equilibrium. A piece of
ice brought near one end of the index cuts offthe influx of heat
to it from that side, and therefore allows an excess of heat to
fall upon it from the opposite side. Attraction by a cold body
is thus seen to be only repulsion by the radiation from the op-
posite side of the i*oom.
Instruments of the kind just described are perhaps the best
for exhibiting large and striking movements of attraction or
repulsion. Two glass globes 4 inches in diameter, fitted up with
bars of pith 3^ x ^ inch, are now before you. One is full of air
at ordinary pressure, whilst the other is completely exhausted.
A touch with a finger on a part of the globe near one extremity
of the pith will drive the bar round over 90^, in the vacuum.
In air the attraction is not quite so strong.
If I place a lighted candle an inch or two from the vacuous
globe, the pith bar commences to oscillate. The swing gradu-
ally increases in amplitude until one or two complete revolu-
tions ar» made. The toraion of the suspending fibre here inter-
feres, and the vibrations pi*oceed in the opposite direction. The
movement continues as long as the candle burns* This con-
tinued movement ceases if the source of radiation is removed
some distance off; the pith index then sets equatorially. The
cause of the continued vibration when the radiant body is
at a particular distance from the pith is easy to understand on
the supposition that the movement is due to the direct impact
of waves on the suspended body.
For more accurate experiments I prefer making the apparatus
differently. Fig. 4 represents the best form, ab is a, glass
tube, to which is fused at right angles another, narrower tube, c d;
the vertical tube is slightly contracted at e so as to prevent the
solid stoper d, which just fits the bore of the tube, from falling
down. The lower end of the stopper de'iB drawn out to a point ;
and to this is cemented a fine glass thread about O'OOl inch
diameter, or less, according to the torsion required.
At the lower end of the glass thread an aluminium stirrup
and a concave glass mirror are cemented, the stirrup being so
arranged that it will hold a beam fg having masses of any de-
sired material at the extremities. At c in the horizontal tube
is a plate-glass window cemented on to the tube. At & is also
a piece of plate glass cemented on. Exhaustion is effected
through a branch tube h projecting from the side of the upright
tube. This is sealed by fusion to the spiral tube of the pump,
Digitized by VjOOQ IC
86 Mr, W. Crookes on Attraction and
The stopper de^ aad the glass plates c and b^ are well fastened
with a cement of resin 8 parts and bee's- wax 3 parts**
The advantage of a glass-thread suspension is that the beam
always comes back to its original position. Before jou is an
instrument of this description^ perfectly exhausted and fitted up
with pith plates at each extremity. A ray of light from the
electric lamp is thrown on to the mirror c, and thence reflected
on to the opposite wall. The approach of a finger to either extre-
mity of the beam causes the luminous index to travel several
feet^ showing repulsion. A piece of ice brought near causes the
spot of light to travel as much in the opposite direction.
Here is another form of the apparatus (fig. 5). The letters
and description are the same as in fig. 4^ the apparatus,
however^ being double. The pieces /, g on the end of one
beam consist of platinum-foil exposing a square centimetre of
surface, whilst the extremities /',y on the other beam consist of
pith plates of the same siec. It Las already been explained that
the neutral point of rarefaction for platinum is much higher than
for pith ; conaequently at a pressure intermediate between these
two neutral points, radiation ought to eause the platinum to
be attracted and the pith to be repelled. This is seen to be
the case. A wide beam of radiant heat thrown in the centre of
the tube on to the plates gyf causes g to be attracted andy to
be repelled^ as shown by the light reflected from the mirrors
Cy c\ The atmospheric pressure in the apparatus is equal to
about 40 millinos, of -mercuiy.
The position of the neutral point not only depends on the
density of the body acted on by radiation^ as in the above case,
but also on the relation of surface to mass. Thus a square cen-
timetre of thin platinum-foil on the extremity of the beam
requires a lower exhaustion for neutrality than a thicker piece
exposing the same surface. Also a flat disk of platinum has a
lower neutral point than the same weight of platinum in the
form of a sphere.
Intensity of radiation likewise affects the neutral point. With
* This is the best cement I have used for standing a Tncuura : for a
few hours it is perfect. But at the highest exhaustions it seems to leak in
the course of a day or two. India-rubber joints arc of no use in these ex-
periments, as, when the vacuum is near upon perfect, they allow oxygenized
air to pass through as readily as the pump will remove it. Whenever
possible the glass tubes should be unitca by fusion ; and where this is im-
practicable mercury joints should be used. The best way to make these is
to have a well-made perforated eonical stopper, cut from plain india-rubber,
^tting into the wide funnel-tube of the jomt and carrying the narrow tube.
Before fitting the tubes in the india rubber this is heated in a spirit-lamp
until its surface is decomposed and vciy stickv ; it is then fitted into its
place ; mcrcurj- is poured over, and oil of vitriol on the top of that. When
well made, this joint seems p^fect.
Digitized by VjOOQ IC
RepuUion accompanying Radiation. 87
pith extremities a point of rarefaction can be obtained at which
the warm fingers repel and incandescent platinum attracts.
Baring the coarse of this lecture I have spoken frequently of
repalsion by heMt^ and have used a spirit-lamp as a source of
h4»t to illustrate the facts described. I now wish to show that
these results are not confined to the heating rays of the spec-
trum, but that any ray, from the ultra-red to the ultra-violet, will
produce repulsion in a vacuum.
In ray own laboratory I have used sunlight, and have experi-
mented with a very pure spectrum, taking precautions to avoid
any overlapping or difi'usion of one part of the spectrum with
another. Here I can only use the electric light, and, in order
to get results visible at a distance, the spectrum cannot be very
long.
The spectrum is formed with one disulphide-of-carbon prism,
and is projected on to the screen by a lens. Immediately be*
hind the screen is an exhausted bulb, having a movable index
with pith terminals suspended with a cocoon fibre (fig. 3). This
is delicate enough to swing over 90^ with a touch of the finger,
and it will even move under the influence of a ray of moonlight.
I first of all arrange the spectrum so that the extreme red would
fall on one pith disk were it not for the screen* On removing
the screen the index immediately retreats, making nearly half a
revolution.
I now replace the screen, and arrange the spectrum so that
the invisible ultra-violet rays are in a position to fall on the pith
disk. On removing the screen the index at once behaves as it
did under the influence of the red rays, and is driven away
twenty or thirty degrees. The action is not so powerful as when
the other end of the spectrum is used ; but this may partly, if
not wholly, be accounted for by the much greater concentration
of energy at the red end of the spectrum, and expansion at the
violet end, when using glass or disulphide-of-earbon prisms.
I now, without disturbing the position of the spectrum, inters
pose in the path of the rays a cell containing a solution of iodine
in disulphide of carbon, which is opaque to the luminous and
ultra-violet rays, but transparent to the invisible heat-rays. Not
a trace of repulsion is produced. The iodine solution is now re-
moved and the ultra-violet rays again fall on the pith, producing
strong repulsion. A thick screen of clear alum cut from one of
Mr. Spencers gigantic crystals is now interposed ; but no efiect
whatever is produced by it, the ultra-violet rays acting with un-
abated energy. As alum cuts off all the dark heat-rays, this
experiment and the one before it prove the suflBcient purity
ef my spectrum.
The spectrum is again turned iditil the dark ultra-red heating
Digitized by VjOOQ IC
88 Mr. W. Crookes on Attraction and
rays fall on the pith. The movement of repulsion is energetic.
The iodine solution, interposed, cuts off apparently none of the
Action. The alum plate cuts off a considerable amount, but by
no means all. On uniting the alum and the iodine solution the
whole of the spectrum is obliterated, and no action is produced,
whatever be the ray which would, were it not for this double
sifting, fall on the pith.
Throughout the course of these investigations, which have
occupied much of my spare time for some years, I have endea-
voured to keep in my mind the possible explanations which may
be given of the actions observed ; and I have always tried, by
selecting some circumstances and excluding others, to put each
hypothesis to the test of experiment.
' The most obvious explanation is, that the movements are due
to the currents formed in the residual gas which theoretically
must be present to some extent even in those vacua which are
most nearly absolute.
Another explanation is, that the movements are due to elec-
tricity developed on the moving body or on the glass apparatus
by the incident radiation.
A third explanation has been put forward by Professor
Osborne Reynolds, in a paper which was read before the Royal
Society on June 18th last. He considers the results to be due
to evaporation and condensation.
I will discuss these explanations in order.
First, the air-current theory. However strong may be the
reasons in favour of this explanation, they are, I think, answered
irrefragably by the phenomena themselves. It is most difficult
to believe that the residual air in a Sprengel vacuum, when the
gauge and barometer are level, can exert, when gently warmed
by the finger, an upward force capable of instantly overcoming
the inertia of a mass of matter weighing 20 or 30 grains. It
must be remembered that the upward current supposed to do
this is simply due to the diminished weight of a portion of the
gas caused by its increase in volume by the heat applied.
An air-current produced by heat may possibly cause the
beam of a balance to rise, may drive a suspended index side-
ways, and by a liberal assumption of eddies and reflections,
may perhaps be imagined to cause these movements to take
place sometimes in the opposite directions ; but as rarefaction
proceeds these actions must certainly get less, and they will
cease to be appreciable some time before a vacuum is attained :
a point of no action or neutrality will be reached. But this
neutral point should certainly be nearer to a vacuum when a
light body like pith, exposing much surface, is under experiment|
Digitized by VjOOQ IC
Repulsion accompanying Radiation. 89.
than when the mass acted on is heavy like brass ; whereas in
practice the contrary obtains. Pith ceases to move under the
influence of radiation at a rarefaction of about 7 to 12 millims.,
whilst brass only ceases to be affected when the gauge and ba-
rometer are appreciably level.
But even could the phenomena up to the neutral point be
explained by air-currents^ these are manifestly powerless to act
after this critical point is passed. If a current of air within 7
millims. of a vacuum cannot move a piece of pith^ certainly the
residual air in a Sprengel vacuum should not have more power;
and a fortiori the residual gas in a perfect chemical vacuum
cannot possibly move a mass of platinum.
It is^ however^ abundantly demonstrated that, in all cases after
this critical point is reached^ the repulsion by radiation is most
apparent ; it increases in energy as the vacuum approaches per-
fection, and attains its maximum when there is no air whatever
present, or at all events not sufficient to permit the passage of
an induction-spark.
I will now refer to the electrical explanation. Very early in
my investigation, phenomena were noticed which caused me to
think that electricity played a chief part in causing the move*
ments. When a hot glass rod is held motionless against the
side of an exhausted tube containing a pith index, repulsion
takes place in a perfectly regular manner; but if the glass rod
has been passed once or twice through the fingers, or is rubbed
a few times sideways against the exhausted bulb, the index im-
mediately moves about in a very irregular manner, sometimes
being repelled from, and at others attracted to, the side of the
glass, where it adheres until the electncal excitement subsides.
Friction with the finger produces the same results; and a small
spirit-flame causes similar, but much fainter, electrical effects. I
soon ascertained, however, that, although electricity is capable
of producing many movements similar to those caused by radia-
tion, they are never so alike as to be mistaken. Electricity fre-
quently interferes with, disturbs, or neutralizes the true action of
radiation ; but it acts in such a manner as to show that it is not
the primary cause of the movement. At the highest rarefactions,
and when special precautions have been taken to avoid the pre-
sence of aqueous vapour, slight friction with the finger against
the bulb, or a touch with the flame of a spirit-lamp, excites so
much electrical disturbance in the pith and other indexes that
accurate observations become impossible with them for several
hours. I have tried many means of neutralizing the electrical
disturbance ; but they are only partially successful, and at the
highest rarefactions interference through electrification is very
troublesome.
Digitized by VjOOQ IC
90 Mr. W. Crookes on Attraction and
I miiy draw attention to the following experiments^ which are
devised with the objeet of showing that the attractions and re*
pulsions are not due to electricity.
In describing the pendulum apparatus (fig. 2) which I set in
motion at the early part of this lecture^ I explained that the
mass of magnesium forming the weight was in metallic con-
tact with the platinum wire which supported it^ and that the
Upper end of this platinum wire was fused into the glass tube
and passed through to the outside. With this apparatus I have
tried a great number of experiments. I hsTc connected the pro-
jecting end of the platinum wire with " earth/' with either pole
of an induction-coil the other being insulated more or less^ with
either pole of a voltaic battery^ with a delicate electroscope ; I have
charged it with an electrophorus^ and have submitted it to the
most varied electrical conditions ; and stilly on allowing radiation
to fall upon the suspended mass^ I invariably obtain attraction
when air is present^ and repulsion in a vacuum. The heat has
been applied both from the outside^ so as to pass through the
glass^ and also inside by means of the ignited platinum wire ;
and the results have shown no diflFerence in kind, but only in
degree, under electrical excitement. I have obtained interference
with the usual phenomena, but never of such a character as would
lead me to imagine that the normal results were due to electricity.
It occurred to me that the repulsion might be due to a deve-
lopment of electricity on the inner surface of the glass bulb or
tube under the influence of the radiation as it passed from the
glass into the vacuum. This appears to be disproved by the
fkct that the results are exactly the same whether the radiation
passes through the glass, or whether it is developed inside the
apparatus as in the above instance.
I have produced exactly the same phenomena whether the
exhausted apparatus has been standing insulated in the air, or
whether it was completely immersed in water connected electri-
cally with " earth,'' or surrounded with wet blotting-paper.
Here are two experiments which bear on this subject. A
straw beam furnished with brass balls at each end is suspended
on a double-pointed needle, and the brass balls and needle
are placed in metallic connexion b^ means of fine platinum wire.
The needle does not rest on the sides of the glass tube, but in
steel cups, to which is soldered a platinum wire passing through
the glass tube and connected with ''earth." The tube is then
exhausted, and the usual experiments are tried with hot and
cold bodies^ both with and without a wet blotting-paper cover.
In all cases the moving beam behaves normally, being repelled
by heat and attracted l^ cold.
An apparatus is prepared similf^r to that shown in fig. 4.
Digitized by VjOOQ IC
Repubiott accompanying Radiation* 91
The inside of the tube ab \% lined with a cylinder of copper
ganse, having holes cut in the centre for the passage of the snp^
porting thread dc and the index ray of light felling on th«
mirror c, and holes at each end to admit of the plates / and g
being experimented with. A wire attached to the copper gause
passes through a hole in the plate b, so as to give me electrical
access to the copper gauae lining. Under the most diverse elec-*
trical conditions^ whether insulated or connected with '' earth/'
this apparatus behaves normally when exhausted*
A further reason why electricity is not the cause of the move-
ments I have described is^ that they are not only produced by
heat^ but also by ice and cold bodies. Moreover 1 shall pi^-
sently show that any ray of the spectrum^ besides those red and
ultra-red rays which produce dilatation of mercury in a thermo-
meter, excite an electric current between antimony and bismuth
couples, and cause a sensation of warmth when falling on the
skin, will produce the effect of repulsion in a vacuum. It is
therefore to my mind abundantly proved that electricity, such
as we at present kuow this force^ is not a chief agent in these
attractions and repulsions, however much it may sometimes in-
terfere with and complicate the phenomena.
I will now discuss Professor Osborne Beynolds's theory, that
the effects are the results of evaporation and condensation.
In my exhausted tubes he assumes the presence of aqueous
vapour, and then argues as follows : — " When the radiated heat
from the lamp falls on the pith, its temperature will rise, and
any moisture on it will begin to evaporate and to drive the pith
from the lamp. The evaporation will be greatest on that ball
which is nearest to the lamp ; therefore this ball will be driven
away until the force on the other becomes equal, after which
the balls will come to rest, unless momentum carries them
further. On the other hand, when a piece of ice is brought
near, the temperature of the pith will be reduced, and it vtill
condense the vapour and be drawn towards the ice."
Professor Reynolds has tried an experiment with pith-balls at-
tached to a light stem of glass and suspended by a silk thread in a
glass flask. The exhaustion was obtained by boiling water in the
flask and then corking it up and allowing it to cool. The gauge
showed an exhaustion of from ^ to | of an inch. The pith-balls
behaved exactly as I have already shown they do at that degree of
exhaustion, heat repelling and iee attracting. He found that the
neutral point varied according to whether air was present with
the aqueous vapour, or whether the vapour was pure water-gas«
Professor Reynolds states v^^" From these last two facts it ap-
pears as though a certain amount of moisture on the balls was
necessary to render them sensitive to the heat. • • • * These ex-
Digitized by VjOOQ IC
92 Mr. W, Crookes on Attraction and
periments appear to show tbat evaporation from a surface is
attended with a force tending to drive the surface back, and
eondensation with a force tending to draw the surface forward/'
It does not appear that Professor Reynolds has tried more
than a few experiments ; and he admits that they were in reality
undertaken to verify the explanation above quoted. I have
worked experimentally on this subject for some years ; and the
last experiment recorded in my notebook is numbered 584.
From the abundant data at my disposal, I can find many facts
which will, I think, convince you that this hypothesis has been
arrived at on insufficient evidence.
In the first place, I will show that the presence of moisture or
of a condensable vapour is not necessary. Besides pith, which from
its texture and lightness might be supposed to absorb and con-
dense considerable quantities of vapour, I have used glass, mica,
and various metals ; and with a proper amount of exhaustion
they all act in the same manner. The fact that the neutral
point for platinum is close upon a vacuum, whilst that for pith
is so much lower, tends to d&ow that the repulsion is not due to
any recoil caused by condensable vapour leaving the surface
under the influence of heat. Were it so, it would certainly
require more vapour to be present when platinum had to be
driven backwards than when pith had to be moved ; but the
contrary obtains in all cases. The rule seems to be, the greater
the density the higher the neutral point.
I have worked with all kinds of vacua ; that is to say, I have
started with the apparatus filled with various vapours and gases
(air, carbonic acid, water, iodine, hydrogen, &c.) ; and at the
E roper rarefaction I find no difference in the results which can
e traced to the residual vapour. A hydrogen vacuum seems
neither more nor less favourable to the phenomena than does a
water vacuum, or an iodine vacuum.
If moisture be present to begin with, I find it necessary to
allow the vapour to be absorbed by the sulphuric acid of the
pump, and to continue the exhaustion, with repeated heating of
the apparatus, until the aqueous vapour is removed. Then and
then only do I get the best results.
When pith is employed as the index, it is necessary to have it
thoroughly dried over sulphuric acid before using it, and during
the exhaustion to keep it constantly heated to a little below its
charring-point, in order to get the greatest sensitiveness.
Professor Reynolds says, '' In order that these results might
be obtained, it was necessary that the vapour should be free from
air.'' On the contrary, I find the results take place with the
greatest sharpness and rapidity if the residual gas consists of
nothing but air or hydrogen.
Digitized by VjOOQ IC
Rqmkion accompanying Radiation. 93
Professor Ueynolds further says^ '' Mr. Crookes only obtained
his results when his vacuum was nearly as perfect as the
Sprengel pomp would make it. Up to this point he had nothing
but the inverse effects, viz. attraction with heat and repul-
sion with cold.'' In the abstract of my paper published in the
Proceedings of the Boval Society, I describe an experiment with
a pith-ball apparatus in which the neutral point is 7 millims.
(about I inch) below the vacuum, repulsion by heat taking place
at higher exhaustions. At the Royal Society SoirSe, April 22,
1874, 1 showed, and fully described in print, the apparatus now
before you, consisting of a pith bar suspended by a cocoon fibre
in a glass bulb, from which the air is exhausted until the baro*
metric gauge shows a depression of 12 millims. below the ba«
rometer. Neither attraction nor repulsion results when radiant
light or heat falls on the pith. Exhaustions of 7 and 12 mil-
lims. are certainly very inferior vacua for a Sprengel pump.
As a matter of fact, however, I have obtained repulsion by
radiation at far higher pressures than these. The true effect of
radiation appeal's to be one of repulsion at any pressure, over«
balanced when a gas is present by some cause — possibly air-
currents, but probably not. I have already explained that the
barometric height of this neutral point dividing attraction from
repulsion varies with the density of the substance on which ra-
diation falls, on the relation which the mass bears to the surface,
and on the intensity of radiation. By modifying the conditions
it is not difficult to get repulsion by radiation when the appa-
ratus is full of air at nearly the normal pressure of the atmo-
sphere.
Professor Reynolds again says, '' The reason why Mr. Crookes
did not obtain the same results with a less perfect vacuum was
because he had then too large a proportion of air, or non- con-
densing gas, mixed with the vapour.'' On this I may remark
that the writer, before he explained how it was I could not get
certain results, should have made sure that what he assumed to
be the case was reallv so. I have not the least difficulty in
showing repulsion by heat in imperfect vacua when mixed va-
pours and gases are present.
In ray arguments against the air- current theory, I have shown
that the best results are obtained when the vacuum is so nearly
perfect that an induction-spark will not pass through it. This
IS an equally good argument against the presence of a conden-
sable vapour as it is against that of air.
From the construction of my Sprengel pump I am satisfied
that the vapour of mercury is absent from the apparatus.
The following experiments have been specially tried with the
object of testing this theory. A tolerably thick and strong bulb
Digitized by VjOOQ IC
94 On Attraction and Repulsion accompanying Radiation.
it blown at the end of a piece of eombnttion-tabing ; and in it
ii supported a bar of aluminium at the end of a long platinum
wire. The whole ii attached to the Sprengel purop, and ex-
haottion it kept going on for about two dayt^ until a tpark will
not past through the raeuuro. During thit time the bulb and
itt oontentt are frequently raised to an incipient red heat. At
the end of that time the tube is sealed off, and the bar of alumi-
nium is found to behave exactly as it would in a lest perfectly
exhausted apparatut; vis. it it repelled by heat. A timilar
experiment, attended with timilar retultt, has been tried with a
glass index. It is impossible to conceive that in these experi-
ments sufficient condensable gat was present to produce the
effects Professor Reynolds ascribes to it After the repeated
heatings to redness at the highest attainable exhaustion (the
gauge and the barometer being level for nearly the whole of the
48 hours), it is impossible that sufficient vapour or gas should
condense on the movable index to be instantly driven off, by the
warmth of the finger, with recoil enough to drive backwards a
heavy piece of metal.
M ^ own impi*ession is that the repulsion accompanying radia-
tion IS directly due to the impact of the waves upon the surface
of the moving mast, and not aecondarily through the interven-
tion of air-currentt, electricity, or evaporation and condentation.
Whether the setherial waves actually strike the substance moved,
or whether at that mysterious boundary-surface separating solid
from gaseous matter there are intermediary layers of condensed
gas which, taking up the blow, pass it on to the layer beneath,
are problems the solution of which must be left to further
research.
In giving what I conceive to be reasonable arguments against
the three theories which have been supposed to explain these re-
pulsions, I do not wish to insist upon any theory of my own to
take their place. The one I advance is to my mind the most
reasonable, and as such is useful as a working hypothesis, if the
mind must have a theory to rest upon. Any theory will account
for some fticts ; but only the true explanation will satisfy all the
conditions of the problem, and this cannot be said of either of
the theories I have already discussed.
My object at present is to ascertain facts, varying the condi-
tions of each experiment so as to find out what are ^e necessary
and what the accidental accompaniments of the phenomena.
By working steadily in this manner, letting each group of expe-*
rinients point out the direction for the next group, and follow-
ing up as closely as possible, not only the main line of research,
but ako the little bylanes which often lead to the most valuable
results, after a tin e the facts will group themselves together
Digitized by VjOOQ IC
Mr. J. O'Kiuealy on Fourier's Theorem. 96
and tell their own tale. The eonditiona under which the phe-
nomena invariably occur will give the laws ; and the theory will
follow without much difficulty! To use the eloquent language
of Sir Humphry Davy, ''When I consider the variety of theories
which may be formed on the slender foundation oi one or two
facts, I am convinced that it is the business of the true philo-
sopher to avoid them all together. It is more laborious to accu-
mulate facts than to reason concerning them ; but one good ex-
periment is of more value than the ingenuity of a brain like
Newton's/'
XIV. Fourier's Theorem.
By James (yKiNEiLY, Bengal Civil Service*.
THE proof given of Fourier's theorem in all the text-books I
know of, is a modified form of that first given by Poisson.
What is at present proposed is to prove it by an analytical pro-
cess for periodic functions, and to show that it is simply the
solution of an exponential differential equation.
l{f{x) =/[x+\), where X is the wave-length, we have, putting
it into the symbolical form,
or
(6^*-l)/(^)=:0.
It is a well-known theorem in differential equations^ that if we
get an equation of the form F(Djr)/(a') =0, and can find the
roots of F (D,)=0, the equation can be put in the form
(D,-«)(D.-«,) (D.-«.).../(*)=0,
where a, a^ a^ &c. are the roots of F(D;r)»0, and that the
solution will be
yt^) = Ae*" + A ,€«»'+ AgC-** .... ,
A, A„ Ag, &c. being constants depending on the nature o{/{x).
In the present case F(Da.) is 6^^*— 1. Assume D^asjsr, and
the equation to solve is
or
or
or
* Communicated by tbe Author.
Digitized by VjOOQ IC
96 Mr. J. O'Kinealy on Fouiier^s Theorem^
(where t is cipher or a positive integer), or
The original differential equation becomes thus
D,.(D.+ ?^X"'- K=^)-/(*)=0,
or
^i \ k . k 27ra? , . Afirx ,
/(a?) :=A + A, COS-r— + AgCOS -r— + . • . .
+ D,8in-:r h B^ Sm -rr- ....
At At
=A+SA,cos^
1=1 X
+ 2B,8in^^.
*=l A,
This is Fourier's theorem ; and, determining the constants in
the usual way by integrating between 0 and \, and by multi-
plying by cos — .r— . sin — — and then integrating, we get the
A. At
usual form,
/W = s: 1 yi^)-^«+r2co8-^-— I f{x) coH-.r— dn
A- Jo ^'=» ^ ^'o ^
2'=« . 2'irix
+ - S sin -^
A| — I A»
j /(^)8in-^-<
In the same way we can obtain other forms of Fourier's theo-
rem. K f{^)=Jlx + h), we have generally f{x)=f{x-{-nh),
where n is an integer; or (c"*^— l)yi[a:)=0, which gives the
same solution as above if we put nX in place of X.
Hence we find
iv \ 1 r% \j . 2 r*^-, ,, 2to V Zirix ^
^^^^X ^^""^ '^^Jo /(^)^«-^^^-nX--^^^^-7iX-^^-
= ^J^ /Wrfn+^^Scos--.J^ /(^).cos— rfn
, 2 %« . 27r?> T"^^ , . 27r/ar ,
The above method of solution may be applied to other some-
Digitized by VjOOQ IC
Oa the Comtant Currents in the Air and in the Sea. 97
what similar forms. Suppose
yi:;s+\)+/(x)=o,
or
The roots of the equation e^^* +• 1 =0 are
where t is any odd integer. Hence
f{x) = 2 A|C08-r-
+ S B| sin-r— J
where t is an odd integer.
Several other theorems of a similar nature will readily sug-
gest themselves as capable of similar treatment.
11 Elysium Row, Calcutta.
XV. T/ie Constant Currents in the Air and in the Sea : an At-
tempt to refer them to a common Cause. JBy Baron N. Scbil*
LING,. Captain in the Imperial Russian Navy.
[Continued from p. 38.]
B. BOTATION OF THE EaRTU ON ITS AxiS.
IN the daily motion of the earth on its axis^ every point of the
surface describes a circle. These parallel circles become
smaller and smaller from the equator to the pole. Now, as all
points of the surface describe their circles in one and the same
time of nearly 24 hours, it is evident that as the poles are ap*
proached the velocity of motion of the points diminishes, and
this in the ratio of the cosines of the latitudes. As already men-
tioned in discussing Hadley^s theory of the trade-winds, a body
approaching the equator, continually coming into circles of
greater velocity, will, in consequence of the law of inertia, have
the tendency to perform its revolution more slowly than these ;
and hence the direction of motion of that body will undergo a
westerly deflection. Conversely, a body moving from the equator
will b^ continually meeting with parallel circles of less and less
velocity, and hence will take a direction swerving eastwards.
Since the commencement of the 18th century the correctness of
this law has been admitted, and it has been made use of to ex-
plain the direction of the trade-winds and many other pheno-
mena. The Academician von Baer, for example, ascribes it to
Phil. Mag. S. 4. Vol. 4S. No. 316. Aug. 1874. H
Digitized by VjOOQ IC
98 Baron N. SclulliDg an the ComtatU Ctarenit
this deviation arising from the eartVs rotation thatj in the
northern hemisphere, all the rivers which run in a meridional
direction undermine their right banks — ^through which these
banks are the high; but the left the low ones. The whirling
motion of cyclones, or Buys-Ballot's law, and the deviation of
the meridional currents of the ocean, are all explained by the
axial rotation of the earth.
It is indubitable that the direction of every independent mo-
tion on the surface of the earth receives, through its rotation, a
certain tendency to deviation; yet it seems to us that the
amount of this deviation is only too often greatly overrated. It
is usually assumed that, in consequence of inertia, air and water
particles can retain for hours the velocity of the paralleb which
they have long left behind. In reality, however, the friction
and resistance of other particles will more speedily overcome the
inertia and comnel the particles in motion soon to take up the
new rotation-velocity of the parallel circles which they enter.
It must also be remembered that the velocity of adjacent paral-
lels only very gradually changes; and therefore, with a slow
motion of the particles, the least friction will be sufficient to
overpower the difference existing between neighbouring parallels.
The true proportion between the friction and the tendency to
conserve the earlier rotation-velocity is very difficult to determine
; iccurately ; nevertheless it seems clear to us that the deviation
thereby occasioned in the direction of motion in a short time
laust always be very inconsiderable. The defenders of Hadley's
theory will admit this, although they generally believe that, by
itself slight, the deviation can, by continual repetition of the
action, accumulate and so become gradually considerable. They
think, namely, that a current of air or sea, originated by differ-
ence of temperature, flowing along the meridian, would, when a
little deflected by the earth's rotation, continue to flow in this
new direction, and so on. In other words, it is generally be-
lieved that the angle which a current makes with the meridian
must continually increase with *the duration of the current ; and
some go so far as to see, not only in the south-west wind of the
middle latitudes of our hemisphere, but even in the north-west
wind of the same, an antipolar current diverted from its direc-
tion by the rotation of the earth. But this evidently false con*
elusion results from the false assumption that a current onoe
deflected would continue to flow in the new direction. It ia
forgotten that the rotation of the earth cannot effect a deviation
of the direction unless a motion is present. If the motive force
ceased to act, the current would soon cease also, being over-
powered by friction and other resistance. It cannot, therefore,
flow further in the deflected direction, but will always again
Digitized by VjOOQ IC
in Uie Air and in the Sea. 99
teek to proceed in the direction in which the force acts that pro-
duces the motion^ therefore in that of the meridian* Now^ ao«
cording to the eiiating theory, two forces are constantly acting
both upon trade-winds and the meridional currents of the ocean t
—-of which the one, the impelling force, springs from the differ-
ence of temperature of the equatorial and polar regions^ and
hence operates only in the meridian-direction ; while the otheri
the rotating force of the earth, acts in coDsequence of the inertia
of the particles, and always in the direction of the parallel circle,
therefore at right angles to the motive force. If, then, both
forces remained constantly unaltered, the direction of the current
would also remain invariably the same; that is, the angle which
the current forms with the meridian would neither increase nor
diminish. In our case the action of the force in the meridional
direction must be assumed to be constantly uniform ; while the
lagging behind, or the advance, called forth by the transition
into other latitudes is more considerable in the higher than in the
lower latitudes, because the parallel circles diminish only very
gradually in the latter, but rapidly in the former. From this
it follows that the deviation from the meridional direction would
necessarily be greatest in the high latitudes, and vice versd.
Every current, of air or sea, springing from difference of tem-
perature would therefore, when flowing toward the equator, come
constantly nearer to the direction of the meridian ; while a cur*
rent flowing away from the equator must be continually adding «
a little to the angle which it forms with the meridian. Accord-
ing to Hadley's theory, the trade-winds, flowing to the equator,
should therefore be continually approximating nearer to the
direction of the meridian; instead of which we see just the op-
posite^— that at thehr polar limit they blow from the north-east or
south-east, according to the hemisphere, and as they near the
equator they come ever nearer to comcidence with the direction
of the parallel drcles.
The sea-currents of the southern hemisphere also demonstrate
that the earth's rotation has but little, if any, influence on the
direction of currents. The warm currents (those of Brazil and
Mozambique^ lean to the east coasts of the continents, and are
directed to tne south-west, instead of deviating eastwards ; while
the cold currents (those of Peru and South Guinea, and the
general current of the entire Antarctic Ocean) agree in directing
their course to the north-east, instead of flowing south-west as
required by the theory of the deviation of direction arising from
the rotation of the earth. We see in this circumstance a proof
that the influence of the rotation is in the whole very little,
although the direction taken by the currents of the northern
hemisphere appears to correspond entirely with that theory:
H2
Digitized by VjOOQ IC
100 BaroQ N. Schilling on the Constant Currents
namely^ the Oulf-stream and the Kurosiwo flow north-east ; and
the cold currents of the seas of Japan and Greenland go aonth-
west, just as the earth's rotation demands. But since the cur-
rents of the southern hemisphere^ notwithstanding the ample
space open to them, are quite unaffected by the rotation of the
earth, we cannot but see that the direction of the currents in the
northern hemisphere must be referred to other causes. The
bend which the Gulf-stream makes again to the north by Cape
Hatteras, after a considerable inclination to the east, seems also
to speak in favour of our view.
If the rotation of the earth deflects the direction of the sea-
currents only inconsiderably, then its influence on the direction
of the rivers can also only be very slight ; but even the slightest
friction of the water flowing along the bank, if constantly re-
peated on one side during thousands of years, must at length
perceptibly undermine the bank ; and hence Von Baer's view
may in this respect be right, notwithstanding the extreme
slightness of the deflection of the current.
On the rotation of cyclones we will speak subsequently.
Besides the action, above considered, upon already existing
currents, many ascribe to the earth's rotation the power to be
independently the motive cause of a current. MUhry, for in-
stance, seeks the force which impels the equatorial stream in the
centrifugal force of the earth. But this, as we know, acts
always in the direction of the radius of the different parallel
circles, and hence cannot possibly either accelerate or retard the
rotation-velocity of the water and the air. Miihry evidently
adheres to Kepler's explanation of the origination of the equa-
torial current, by the water staying behind the general motion
of the earth. This, however, contradicts all the laws of mecha-
nics, and is therefore quite inadmissible. The water and the
air adhere to the globe by the pressure of their weight, and
must, in the course of the thousands of vears during which the
earth has turned on its axis, have very long since attained the
same velocity, through friction, since velocity once acquired is
not again lost so long as there is no resistance. The perma-
nence of the earth's rotation, however, sufficiently proves that
in the universe no such resistance is present. The phenomena,
too, of both air- and ocean-currents absolutely contradict the
assumption that the water and air are subject to a slower rota-
tion than the earth itself.
If this assumption were correct, the atmosphere, being less
dense, must be far more exposed to the action of the retardation
than the water, and over the entire surface of the earth wc
should constantly have strong east winds. Besides, although
decreasing from the equator to the poles; the retardation wo^d
Digitized by VjOOQ IC
in the Air and in the Sea. 101
yet be perceptible everywhere. But this is by no means the
case. At the equator itself^ or in its vicinity^ no such current
is to be observed either in the air or in the water; nay^ in the
equatorial zone we find that the sea has a slight current flowing
east ; so that here, not only is no retardation to be traced, but
the water moves faster than the earth turns. In the zones of
the Sargasso-seas, again, and in the calms of the tropics, in both
hemispheres, neither in air nor sea can any diminution of the
rotation-velocity be perceived. Farther polewards, especially
between the 40th and 50th parallels of latitude, the constant
west winds and currents flowing east testify that water and air
move eastwards more rapidly than the earth rotates. This cur«
rent in the atmosphere in the middle latitudes is explained by
the anti-trades, of which we have already spoken. It expresses
itself in the sea just as it does in the atmosphere ; but as the
anti-trade explanation is absolutely inapplicable to the water>
Miihry accounts for the sea-current by the aspirating force of
the equatorial stream. Why, however, this force has no action
at all upon the zones of the Sargasso-seas, but goes round them
in a wide arc, remains unexplained. Thus, for example, in the
South Atlantic the action of this aspirating force stretches along
the coast as far as the Cape of Good Hope, and thence across
the ocean to the American shore. If the aspirating force of the
Atlantic equatorial current were actually so great that its influ-
ence could make itself perceptible not only to the Cape of Good
Hope, but also from there to the American coast, then it could
not fail to lay bold of the Mozambique current at the Cape and
lead it into the Atlantic to supply the equatorial stream. Yet,
as is well known, at the Cape of Good Hope the Mozambique
cunrent makes a strikingly sharp bend to the east, and returns
on a wide circuit to compensate the equatorial stream which
flows in the southern part of the Indian Ocean, after first wash*
ing the west coast of Australia. The insufficiency of the expla-
nation of currents by aspiration presents itself so distinctly that
it is scarcely necessary to dwell longer on the subject.
The earth's rotation cannot, then, generate any currents in air
or sea; it can only effect a slight tendency of the freely moving
air- and water-parcicles to shift their direction towards that of
the equator. This tendency, however, is so feeble that from it
no perceptible current can arise; hence we have not touched
this point in the Russian edition of this work. We will never-
theless more closely consider here the action of the centrifugal
force.
Every rotating motion, and therefore also that of the earth
about its axis, generates a centrifugal force. The quantity of
this force for every single point of the earth's surface is readily
Digitized by VjOOQ IC
102 Baron N. Schilling on the Comiani Currents
jl^termined by dividing the tqnare of its rotational velocity by
the radius of its uarallel circle. It thence follows that the oen*
trifugal force of the earth is greatest at the equator (0*11124 foot
in a second)^ and from that to the poles it diminishes in the
ratio of the cosines of the latitudes. By its action every thing
on the surface of the earth would be thrown off, if the earth's
gravitation were not greater than its centrifugal force. Now
kt us suppose the gravitation of the earth to cease to act during
one second. Every particle not firmly adherent to the earth
would instantly leave the surface and continue its motion in the
direction of the tangent of the corresponding parallel circle with
its previous rotational velocity; and the relative distance of the
particle at the end of the second, from its point of separation,
which the rotation has meanwhile carried forward on the earth's
surface, would serve as an expression of the quantity of the cen<-
trifugal force of the corresponding parallel circle.
Thus, if a particle at A (fig. 1) were no longer subject to the
Fig. I.
earth'sg^vitation,it would
oontinuo its motion in the
direction of the tangent
AM, and after the lapse
of a second would arrive
at M instead of at B. A,
the point at which it was
discharged, would mean-
while have reached B; and
B M would denote for us
the centrifugal force cor-
responding to the parallel
circle ABD. Now in
reality the action of gravi*
tation never ceases, but is
constantly directed to the centre of the earth, therefore at a
certain angle to the direction of the centrifugal force B M. A
freely displaceable particle of the surface would thus, under the
action of the two forees, after the lapse of a second not be at M,
but would slide on the surface of the earth to F, if there were
no friction or other resistance. Eveiy particle of water or air,
being free to move, must thus have a tendency to recede from a
particle (B) firmly adherent to the earth, and to approach the
equator in the direction of the meridian. This tendency is ex-
pressed by the quantity BF, which is equal to BM. sin BMP,
or the centrifugal foree of the parallel cirele multiplied by the
sine of the latitude. The centrifugal force
BMsiC.cos^,
Digitized by VjOOQ IC
m the Air and in the Sea. 108
where C denotes the eentrifagal force of the equator, and ^ the
latitade of the parallel circle. Consequently BF n= C . cos ^ . sin (f>,
and therefore reaches its maximum quantity when ^=45^,
•monnting then to sin*45^x 0*11124 foot 3:0*05668 foot in a
second^ or 4806*4 feet in 24 hours (which makes 1^ verst,
nearly y of a Oerman^ or almost exactly ^ of a British statute
mile). This inconsiderable tendency toward the equator is
farther diminished by friction, and therefore cnnnot possibly be
thought of as the inotive force of a current. Yet it may per-
haps contribute something to this — that in each of the oceans
the current flowing^ in the middle latitudes^ from west to east
gradually inclines in its direction a little to the equator. .
The earth's centrifugal force, acting in an opposite direction
to that of gravity, occasions over the entire earth, with the
single exception of the two poles, a more or less perceptible di-
minution of weight. This is greatest at the equator, amounting
to nearly the 290th part. Thence to the poles the quantity to
be deducted from gravity diminishes in the ratio of the squares
of the cosines of the latitudes. Now, as all bodies (air and water
not excepted) are somewhat lighter in the vicinity of the equator
than in higher latitudes, one would think that this must pixnluce
currents in the ocean and atmosphere equal to those arising from
the lightening of the water and air by heating. These currents
must flow beneath to the equator, and as upper currents from
the equator to the poles. But in reality this does not appear to
be the case; for degree-measurings and pendulum-observations
have shown thai the surface of the sea has the form of an ellip*
toid slightly compressed at the poles, the long diameter of which
(measured in the plane of the equator) is ^^^ of its length
greater than the shorter diameter (measured in the line of the
earth's axis). From this we see that the level of the ocean at
the equator is nearly as much raised as the weight loses there
through the action of the centrifugal force; hence probably
none, or a scarcely perceptible portion of the lighter water at
the equator can flow off.
It is, perhaps, just the same with the atmosphere; yet it is
probable that, with diminished pressure, the strong elasticity of
the air will produce by expansion a greater raising of its level
(if such an expression can be used) than the centrifugal force
requires. If it is so, certainly the upper, much rarefied air
liiust flow off from the equator, and be replaced by an under-
current. Now, since the mass of the inflowing and of the out-
flowing air must be the same, the dense undercurrent will be
considerably less perceptible than the upper strongly rarefied
one. The centiifugal force may thus, combined with the differ-
ence of temperature^ generate the currents in the upper strata
Digitized by VjOOQ IC
104 Baron N. Schilling on the Constant Currents
of the tropical atmosphere^ and bo also exert a certain influence
on the trade-winds^ bnt cannot possibly develop sufficient force
to give rise to those winds.
We conclude the consideration of the influence of the eartVs
rotation on air- and sea-currents with the conviction that the
existing explanations are altogether insufficient for the currents
which flow parallel to the equator, because the rotation of the
earth can only inconsiderably alter the dii*ection of an already
existing current, whether in air or sea, but can never indepen-
dently produce a current of any importance.
C. Attraction op the Sun and Moon.
As is known, all the heavenly bodies attract each other, the
force therein developed being, according to the law of the im-
mortal Newton, directly as the mass and inversely as the square
of the distance between the two bodies. If, therefore, we take
as the unit of mass that of the earth, and as unit of distance the
semidiameter of the earth, then, according to Newton's law, the
force with which the sun attracts the earth's centre will be ex-
pressed by ■ g. The moon attracts the centre of the earth
with the force kph^f^q*' The ratio of the attractive force of
o\J[0\)y
the 'other heavenly bodies will be readily found in the same
manner. For example, the force with which Jupiter attracts the
earth when nearest to it is one 25th part of that of the moon.
The action of all the rest of the heavenly bodies, so vastly dis«
tant, is again considerably less.
Now, as the force with which a given heavenly body (the sun
for instance) attracts the earth depends entirely upon the dis-
tance between the two, it is self-evident that the parts of the
earth's surface which are nearer to the sun must be exposed to a
greater attraction than those more distant. This can have no
effect on the solid surface of the earth ; but the easily displace-
able particles of the sea and the atmosphere must nave their
equilibrium destroyed by its influence; and to restore the equi-
librium currents must arise. In order to form true ideas of
these currents, it is absolutely necessary to investigate more mi-
nutely the forces which call them forth, and the action of these
forces. Before all things we must realize that we wish to con-
* We have assumed, after Klein (Das Sonnensystem), that the mass of
the sun is 319500 times, and that of the moon one 80th part of that of the
earth. For the mean distance, wc have assumed that tlie distance of the
sun is 390 times that of the moon, whot^mean distance we estimate at 60
•emidiameters of the earth.
Digitized by VjOOQ IC
in the Air and in the Sea.
105
gidcr^ not tlie absolute motion of each particle^ but only the re-
lative motion of the particles with respeet to the earth's centre.
Hence we have not to do with the whole of the attraction whibh
any heavenly body exerts on the earth ; the difference between
the forces with which the earth's centre and the point of its sur-
face to be considered are attracted gives the limits for our consi-
deration. Thus^ e.ff., the point which has the sun or the moon in
the zenith is nearer to this heavenly body than the centre of the
earth ; and the difference of the attraction upon these two points
. , , , , , 819500 819500 - ,, , ,
might be expressed by -^g^^i - J234mj^ *""' ^
80(59)* "^ 80(60)* ^^^ ^^^ ""^°' The second quantity is equal
to about 2^ times the first ; and from this we infer that although
the attraction of the sun is 168 times that of the moon^ yet the
difference between the attraction of a point at the surface and
the centre of the earth by the moon is greater than the same by
the sun; and therefore the effect produced by her attraction
upon the currents of air and sea must also be greater.
For all other heavenly bodies this difference is so slight that
we need not take it into consideration.
Supposing that the circle ACED (fig. 2) represents the
Fig. 2.
/
'^
"V
/
K
H
P
jw ^ 1
\
/
/
earthy L the place of the centre of the moon or sun^ and that k
denotes the difference between the attraction of a point at the
surface and the centre of the earth. The point A is attracted
more strongly than the centre by the quantity k^, Now^ as this
attraction in the half of the earth turned towards the sun or
moon acts in the opposite direction to the earth's attraction,
^— it, will express the weight of any particle in the point A, the
earth's gravitation being denoted byy. At the point B the dif-
ference between the attraction of it and the centre will be some-
what less. Let us call this, difference k^; then the weight at
the point B may be expressed by ^— Ar^.cosLBA; for here the
Digitized by VjOOQ IC
106 Baron N. Sohilling on the Constant Currents
attraction of the moon acts at the an^le LBA with the earth's
gravitation. We thus see that the weight of the water and air
becomes greater the further we remove from the point where
the moon or the sun is in the senith. In the points C and D,
which are as distant as the centre of the earthy A=0; therefore
the full attraction of the earth corresponds to the weight of the
water and air in these points. In the other hemisphere, turned
away from the moon, A is a negative quantity, because the centre
of the earth is more powerfully attracted than any point of the
surface of this hemisphere. But k acts in the same direction
with gravitation, and must therefore be added to it in order to
determine the weight of a particle in this hemisphere. The
point E, most remote Arom the moon, is the most feebly attracted ;
hence in £ also the quantity to be added to gravitation is the
least, and the weight of a particle in E lighter than in any of the
other points of the hemisphere which is turned away from the
moon. In the point F, tor example, the weight of a particle
might be expressed by^— A:3 • cos OFL ; and it would constantly
diminish the more we approached the point E, which has the
SUB or the moon in the nadir, where its expression would be
ff-^k^' When the sun is in question, k^ is only slightly less
than k^ ; but the difference is not insignificant when the attrac-
tion of the moon is taken into consideration ; the difference be-
tween the attraction of the point which has the moon in the
zenith and that of the centre of the earth is 1^ the difference
between the attractions of the centre and the point which has
the moon in the nadir. Briefly, in each of the two hemispheres
(one turned to the sun or moon, and the other turned from it)
the minimum of the weight is found in the point of the surface
which has the sun or moon in the zenith or nadir, but the maxi-
mum on the line D M G N, which divides the two hemispheres.
The pressure of the greater weight must cause a portion of the
water and air to flow into the region where water and air arc
lighter ; and hence a raising of the level will take place there,
corresponding to the less weight, while in the region of the
greatest weight the level will sink. Consequently both the sea
and the atmosphere must endeavour to take the form of an ellip*
■oid the summits of which are on the line which passes through
the centre of the earth and the moon. By the action of the suu,
as by the moon's attraction, an ellipsoid somewhat less elongated
will be formed in the sea and the atmosphere, its major axis
being on the line which passes through the centre of the earth
and the sun. In reality the actions of these two attractions
will be combined and form only one tidal ellipsoid, which is most
ekmgmted when the actions of the sun and moon coincide--that
is, at the timet 9f full and new mp^Dr On the contrary, the
Digitized by VjOOQ IC
in th Air and in the Sea. 107
ytising of the level will be less when* the major axes of the two
dlipaolda are perpendicular to each other — that ii^ at the timet
of the first and last quarters of the moon.
All this we see confirmed in nature by the phenomena of ebb
and flow of the tides. Many renowned mathematicians (among
whom Newton^ Euler^ Laplace^ and Airy occupy the first place)
have endeavoured to determine by very ingenious mathematical
calculations the laws of the tides ; their theories^ however^ do not
in all respects perfectly agree with the phenomena. We find,
for instance, that on the coasts of the islands in mid*ocean the
tide often rises only a few inches^ and seldom amounts to more
than from 2 to 8 feet, while one would think that it was just in
the open ocean that the tide could be fully developed. Accord-*
ing to the theory, the tide should assume the greatest dimen*
sions in the tropical regions—instead of which, we find that,
with very trifling exceptions, it is very moderate in the tropics,
and does not reach, by a long way, the height it attains in the
English Channel or on the coasts of the Bay of Fundy in Nova
Scotia. Airy based his tide-theory on the theory of waves, and
hence ascribes to the water-particles only a vertical oscillating
motion. But, self*evidently, there cannot be anywhere an ele«
vation of the sea*face, unless the necessary water flows to the
Ci% of elevation, water being incapable of elastic expansion ;
ce, among tidal phenomena, the existence of a horisontal
motion of the water is undeniable. Nay, the horizontal motion
must be very considerable, since it is dble, in the course of a
few hours, to call forth a not unimportant elevation of the
water-surface over many thousands of square miles.
If the earth stood still and the same points had the sun or
the moon in the senith constantly, the surface of the sea would
probably take the position of the tidal ellipsoid given by the
theory, and always retain the same form. But now the relative
position of the sun and moon to the earth is perpetually chang-
ing through the rotation of the latter ; and therefore a very
large volume of water and air must continually flow out of one
part of the ocean into the other, in order to compensate thefar^
extended disturbance of equilibrium.
Now, as the relative change of place of the sun and the moon
i s very rapid, while for the complete formation of the tidal ellip*
aoid a certain time is necessary, it may be that the ellipsoid has
not sufficient time to take its perfect form ; the tendency, how-
ever, to form it must call forth currents in air and water, which
will constantly follow the motions of the moon and the sun. If
this be admitted, it explains to us why, in the open ocean, where
these currents proceed undisturbed, no tide, or a very slight on^
is observed j for only whe]:e insufficient depth ox the shi^ of
Digitized by VjOOQ IC
108 Baron N. SchilliDg on the Constant Currents
the coast detains the current which follows the sun and the
moon must the water more or less swell, and thereupon, in aa
undulatory motion, push the swelling further, in accordance with
the law of the wave-theory, and in this manner carry the tide
into high latitudes, whither, according to the theory of the
moon's attraction, it should not come.
We are confirmed in this view of the tides by the circumstance
that the tide* wave in the atmosphere has not yet been observed,
although according to the theory it must show itself there more
considerable than in the sea. The question of the atmospheric
tide-wave has occupied many scientific men. Laplace, after a
long series of observations, expressed a decided opinion that
there is no atmospheric tide. More recently Bouvard, Eisenlohr,
and Sabine have thought they could perceive a very small tide,
expressing itself only m hundredth parts of a line on the baro-
meter-scale*
By the way we must remark that the mercury of the barome-
ter, just like all other bodies on the earth's surface, loses a por-
tion of its weight by the attraction of the moon and sun ; so
that it cannot show the variation of the atmospheric pressure
produced by the attraction of the moon, so long as the mass of
air above it remains the same ; every current, however, must
alter the height of the mercury column. It is just the same
with respect to the diminution of weight effected by the centri-
fugal force. An aneroid, as such, is not exposed to these influ-
ences, and therefore always gives the absolute pressure of the
atmosphere ; so that in principle it is preferable to the barome-
ter. In practice, however, it still needs considerable improve-
ments, because errors arise from the metal not possessing per-
fect elasticity. It is to be wished that observations of the two
instruments were more frequently compared.
It was not until the present memoir had already appeared in
Russian that I got a sight of the extremely interesting and in-
structive treatise on Tidal Phenomena by Dr. Schmick. This
writing (which, while throwing much light on the phenomena
of the tides, contends for many views to which we cannot assent)
well deserves a closer consideration than would be in place here.
Yet we cannot omit to say a few words on his notion of the dis-
placement of the earth's centre of gravity. Since the height of
the tide-wave is greater in the hemisphere turned towards the
moon or sun than in the opposite one, Ur. Schmick thinks that
the centre of gravity of the earth is displaced somewhat towards
the side of the greater gathering of waters, and that the earth
cannot by its own force recover its original centre of gravity
after it has suffered displacement from without. A constantly
repeated displacement^ in this way, of the centre of gravity
Digitized by VjOOQ IC
in the Air and in tie Sea. 109
in the direction of the southern hemisphere occasions there^
according to Schmick^ an accumulation of the waters. That
the centre of gravity, displaced by external force, cannot of
its own accord resume its former position is perfectly true;
only Dr. Schmick seems to have forgotten that if the water
rises higher on the hemisphere turned towards the moon than
on the opposite, it is because it is lighter there on account of the
greater attraction of the moon, and a greater gathering of the
lighter water is necessary in order to restore equilibrium, with*
out displacing the centre of gravity. If, therefore, the entire
globe consisted of a liquid and had no rotation, the moon's at-
traction would cause it to take the form of an ellipsoid, of which
the cusp directed to the moon would be somewhat higher than
the cusp turned away from it; but the centre of gravity of the
entire mass would remain undisturbed in its old place, because,
as already said, the rise of the water on each point must be
exactly equivalent to its loss of weight. As, however, the earth
consists, for the most part, of a solid mass, which cannot alter
its shape, and the hemisphere turned to the sun and moon loses
more of its weight than the opposite one, the centre of gravity
must be displaced in the opposite direction to that supposed by
Dr. Schmick ; namely, it must remove to a somewhat greater
distance from those bodies. Of course the displacement is only
very inconsiderable, even when the moon is at its least distance
from the earth ; yet it may to some extent favour temporary
variations of the atmospheric pressure. In the moon, which
constantly shows one side to the earth, the earth's attraction
must thus cause the centre of gravity to lie permanently on the
side which is turned away from us.
When the tidal wave does not attain its greatest height at the
time required by the moon, or in consequence of collateral cir-
cumstances attains a far greater height than the moon's at-
traction demands (as in the Bay of Fundy, the English Channel,
and many other places), the earth's centre of gravity will cer-
tainly remove temporarily in the direction of the elevation of the
waters; but Schmick's view*, that the water must spread over
the surface in accordance with the new centre of gravity as soon '
as the accumulating force ceases, cannot be regarded as correct,
because any excessive accumulation of the water is. followed by
an equal sinking of the level. The earth's centre of gravity
must follow these oscillations of the water, and hence, when this
gradually comes to rest, will probably have returned to its old
position.
[To be oontinued.}
• Fluth^Phanmene, p. 128.
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[ 110 ]
XVI. Apparatus for Measurement ^L(nvPrei9ur^qfOai. Bv
TrofeuorWLzoD, Indian CivU'Engmeermg CoUei,e, Coopefs
HillK
THIS apparatus was devised for estimating the pressure of a
gas when its tension is so low that the -^r--^^
indications of the barometer cannot safely
be relied on, unless indeed a very wide
barometer and an accurate cathetometer
be employed. The method consists in con-
densing a known volume of the gas into
a smaller space and measuring its tension
under the new conditions.
The form of the apparatus is the follow-
ing J — The tube a communicates with the
Sprcngel, and with the apparatus to be ex-
hausted ; J is a siphon-barometer with a
tube about 5 millimetres in diameter ; and
the principal parts of the measuring-appa-
ratus consist of c, a globe of about 48 cubic
centims. capacity with the volume-tube at
the top, and d the pressure-tube; these
two are exactly of the same diameter, to
avoid error from capillarity. The tube at
the bottom of the globe is ground into a
funnel-shaped portion at the top of the
wide tube e ; and to the side of the latter
the pressure-tube d is joined. The volume-
tube at the top of the globe is graduated
in millimetres from above downwards, the
lowest division in this particular apparatus
being 45 ; the pressure-tube d is also gra-
duated in millimetres, the 0 being placed
at the level of the 45th division on the vo-
lume-tube. A ball-and-socket joint con-
nects the bottom of e with a vertical tube
/ about 800 millims. long, which is con-
nected at its lower extremity by means of
a flexible tube with the mercury-reservoir g ;
a stopcock at h permits the regulation of
the flow of mercury into the apparatus:
this may be conveniently turned by a rod,
so that the operator may watch the rise of
♦ Read before the Physical Society, June 13, 1874.
the Society,
Ccirirvnicated by
Digitized by VjOOQ IC
On an Apparatus far Meaiurement of Low Presiurei of Gas. Ill
tlu^ mereury through a telescope and have the stopoook at the
same time at command,
Ti'.e volume-tube was calibrated in the usual way^ by intro«
ducing weighed quantities of mercury into it^ and making the
necessary corrections for the meniscus. The capacity of the
volums-tube, the globe^ and upper part of the tube e was
determined by inverting the apparatus and introducing mercury
through e until the mercury flowed down the pressure-tube |
the weight of this quantity of mercury, divided by the weight of
that contained in tne volume-tube^ gives the ratio between the
volumes; in tlie present case it is 1 to 54*495. While the appa^
ratus is being exhausted^ the reservoir ff is lowered so as to
prevent the mercury rising out of the tube /; but when it is
desired to make a measurement of the pressure^ the reservoir is
raised and the mercury allowed to pass through the stopcock h.
On the mercury rising into the tube e it cuts off the communi-
cation between the gas in the globe and that in the rest of the
apparatus. Ultimately the whole of the gas in the globe is con-
densed into the volume-tube ; and its tension is then found by
measuring the difference of level between the columns of mercury
in the volume- and pressure-tubes. On dividing this difference
by the ratio between the capacities of the globe and volume-tube,
a number is obtained which is approximately the original pres-
sure of the gas; this number must now be added to the differ-
ence between the columns, since it is obvious that the column
in the pressure-tube is depressed by the tension of the gas in
the remaining part of the apparatus ; on dividing this new num-
ber once more by the ratio between the volumes the exact
original tension is found.
An example will best illustrate this. A quantity of gas was
compressed into the volume-tube, and the flow of mercury was
arrested when its surface reached the lowermost division on the
tube. The volume was then ^.\ ^-= of its original volume, and
54*49 5 " .
the difference between the levels of the mercury m the volume-
and pressure-tubes was 66*9 millims. ; this number, divided by
54*495, gives 1'228 as the approximate pressure. 1*2 must
therefore be added to the observed column, which thus becomes
68*1 ; and on dividing by 54*495, the number 1*2497 is ob-
tained as the actual pressure.
The relations existing between the contents of the other divi-
sions of the volume-tube and the total contents of the gk)be
were determined by measuring the tensions of the same quantity
of gas when compressed into the different volumes. By this
means the values of the divisions 40, 85, 30, 25, 20, 15, 10, 9,
8, 7, 6, 5, 4, 3, and 2 have been found ; the experimenter is
thus enabled to employ a division suitable to the quantity of gas
Digitized by VjOOQ IC
112 On an Apparatus for Measurement of Low Pressures of Gas.
with which he has to deal. The Bmallest division contains oq)/
149^2-35 ^^ ^^^ globe ; consequently when a quantity of gas
hf^ been condensed into this space^ its original tension wil! be
multiplied 1492*35 times. In one case an amount of gas, w'aich
originally filled the globe^ exhibited a pressure of onl^ *5 m' llim.
when it had been compressed into the smallest dinsion c f the
volume-tube ; this indicates an original pressure of only *00033
millim.
When measuring a tension^ it is advisable to make two read-
ings under different condensations, and to take the mean of the
results. The foUowbg will give some notion of the precision
attainable :—
I. At division 5 -0225^ -kr^^ .noQn
„ 2 -0235/ Mean -0280.
Mean -0232.
Bemeasured.
At division 5 -02281
2 -0236/
II. Barometer 0 millim. : —
At division 10 -igSSl fuf ^^ .moo
5 -1980/ Mean -1982.
Remeasured.
At division 10 •1953\ t., ,^^^
6 -1967/ Mean -1960.
III. Barometer 0*6 millim. :—
At division 15 •5488*]
„ 10 -5488 y Mean -5492.
„ 6 •550lJ
Remeasured.
At division 15 •54641
„ 10 -5464 y Mcau 5469.
„ 6 •5480j
IV. Barometer 1 millim. : —
At division 20 1-20421 ^ .^^.^
„ 15 1-2069/ ^^" ^ '*"^^-
Bemeasured.
At division 20 1-20821 ^i- , ^^^
„ 15 1-2099/ *'^^ 1-2090.
V. Barometer 1*5 millim. : —
At division 30 1-91391 t^ i.mAn
„ 25 1-9080/ Mean 1-9109.
Bemeasured.
At division 30 190411 t.^ , ^^.^
„ 25 1-9039/ M^^ ^'^^'
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Dr. W. H. Stone on Wind-pressure in the Human Lungs* 113
VI. Barometer 2*1 millims.: —
AtdivisioaSS 2-60171 Mean 2-6045
80 2-6078/ ^^^*^ ^ ^"^•
Remeasured.
At division 35 261601 ^ o.., ^
30 2-6220 J ^^" ^ ^^^•
It may be mentioned incidentally that connexions for appa<»
ratus may be conveniently made by means of balKand-socket
joints of glass. The ball is made by thickening a piece of tube
in the bWpipe-flame^ and the socket by cutting in half a thick
bulb blown on a glass tube. The ball is then ground into the
socket by means of emery and solution of soda^ and afterwards
polished with rouge and soda solution. When slightly greased
and with a small quantity of mercury in the cup, a joint is ob<«
tained which is perfectly air-tight and flexible*.
XVII. On Wind-pressure in the Human Lungs during Perform^
once on Wind Instruments. By Dr. W, H. Stone f.
THE object of these experiments was originally physiological.
It had been stated by many writers that the forced expi«
ration employed in playing tended to produce emphysema of
the lungs ; but the real amount of such pressure had never
been measured.
The facts elicited had also an interest of a purely physical
character, which was the principal cause of their being brought
before this Society, although, the writer of the paper remarked,
it was on the border-ground between two great subjects of study
that new phenomena were often to be looked for.
The experiments were two in number. The first aimed simply
at measuring, by means of a water-gauge, the extreme pressure
which could be supported by the muscles of the lips, both in
trained musicians and in persons unaccustomed to the con-
tinuous exercise of these organs. The difference between dif-
ferent individuals was very great, some untmined persons
having naturally considerable muscular power. About 6 feet
of water was the ordinary maximum when a small tube was
* Since the above was written Dr. Sprengel has pointed out that Mr.
Hartley (Proc. Roy. See. vol. xx. p. 141) has descnbed as a ''Sprengel
joint " a connexion between two glass tubes made by grinding a conical
tube into a conical cup and placing mercury or water in the cup. The
difference between this and the one above mentioned is obvious: the
former is quite rigid, the latter perfectly flexible.
t Read before the Physical Society, April 18, 18/4. Coiumunicated
by the Society.
PhU. Mag. S. 4. Vol. 48. No. 316. Aug. 1874. I
Digitized by VjOOQ IC
1 14 Dr. W. H. Stone on Wind-pressure in the Human Lungs.
inserted between the lips. When the lips were sapported by a
cupped mouthpiece, such as is used for brass instruments, a
greater height of the column could be obtained. The great
majority of untrained persons could not support more than
three or four feet of water. It was to be noticed that the lip-
muscles invariably gave way long before the expiratory power
of the thoracic muscles was exhausted. By pinching the lips
round the orifice of the tube with the hand, and thus prevent-
ing their yielding, a far higher column of water could be
supported.
The second experiment consisted in introducing a small bent
glass tube into the angle of the mouth, connected with a flexible
tube passing over the shoulder. It was found that most instru-
ments could be played as well with this addition as without it.
It obviously established a communication between the cavity of
the performer's mouth, and therefore of his thorax, and the
pressure-gauge. The following Table was compiled from many
observations on some of our principal English musicians. The
person experimented on was placed with his back to the gauge,
the small tube was inserted in his mouth, and he was directed
to sound in succession the chief notes of his instrument. As
soon as the tone became full and steady, the position of the
water-gauge was noted. A fair " mezzo-forte " note was em-
ployed. Of course, by forcing the wind and overblowing the
instrument, much greater pressure could be obtained; but those
given here were sufficient to produce an average orchestral
tone.
Oboe . .
• lower notes
9 inches ;
highest 17 i
nch
Clarinet .
• 99
15
fy
,1
8
„
Bassoon
• 9f
12
99
f9
24
fi
Horn . .
if
5
Jl
1>
27
99
Comet . .
}}
10
99
99
34
99
Trumpet .
• }f
12
99
99
88
99
Euphonium
• it
3
1>
99
40
|>
Bombardon
• 9}
3
99
99
86
99
It is to be noticed that the clarinet, in this as in some other
respects, differs from its kindred instruments — and also that
most of the pressures are small, not exceeding or, indeed, attain-
ing the pressure of a fit of sneezing or of coughing. They are
therefore very unlikely to injure the lungs, or to produce the
emphysema erroneously attributed to them.
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C 115 ]
XVIII. On the Fall in PUch of Strained Wires through which a
Galvanic' Current is pasting^ By Dr. W. H. Stone*.
THE object of this paper was to apply tbe vibrations of sound
to the measurement of electrical currents^.and to distin-
guish what was due to heating-effects from those caused by
alteration of elasticity.
Strings of brass and steely such as are used for pianofortes
(No. 16 gauge)^ were stret^hed^ by means of wrest-pins^ across
a resonant box^ over bridges surmounted by brass bearings^ and
tuned to unison. On passing a current fi*om two or more
Grovels batteries through them, a very marked fall in pitch wa?
obtained. The vibrating string being 24 inches long, and tuned
to two-foot C, the tone sank above a fourth in steel and a major
third in brass.
This result being a compound of actual lengthening by heat
and of other causes, it was, in a second experiment, endeavoured
to eliminate the former element by straining similar strings
between the same bridged by means of a weight. This was
attached to the arm of a bent lever, to the short end of which
the string was made fast. By shifting the position of a four^
pound weight along the arm, very accurate unison, or definite
periodicity of beats could be obtained. When the curi*ent from
the battery was passed through this string, free to expand by
the falling of the weight, and therefore at a constant tension, a
fall of pitch was still noticed. There was also a very marked
loss of tone, which,* on approaching a red heat, amounted to
total extinction of sound.
A third experiment exhibited the changes of electrical resis-
tance in a wire subjected to variations of strain. The wire wlas
accurately balanced against another resistance in a Wbeatstone's
bridge, and the spot of light from a mirror-galvanometer join-
ing the two circuits thrown on the screen. On suddenly in-
creasing the tension and raising the musical pitch of the string,
the galvanometer was visibly deflected. This was not an effect
of heat (since the balance nad been brought about during the
passage of the current), and must be due to altered molecular
state caused by the strain.
It was incidentally noticed that, when beats were produced
by two strings on the same sonometer, they continued to be
sensible to the touch by laying the hand on the instrument long
after, from diminution of amplitude in the vibration, or from
slowness in the beats themselves, they had ceased to be audible,.
This afforded a good demonstration of the continuity of sensa-
tion in touch and hearing.
* Read before tbe Physical Society, May 9, 18/4. Communicated by
tbe Society.
12
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[ 116 ]
X[£, On an Improvement in the Construction of the Spectroscope.
By H. G. Madak.
To the Editors of the Philosophical Magazine and Journal.
Gentlbmen^
IN the ' Proceedings of the Royal Society/ No. 152, p. 808,
there it an account by Mr. Grabb of a very satisfactory
method of correcting the curvature of the spectrum-lines, a de«
feet inherent in all spectroscopes as at present made. This dis-»
tortion is due, of course, to the fact that the rays from different
parts of the slit fall on the prism under different vertical angles ;
and Mr. Grubb proposes to correct it by making the slit itself
curved instead of straight, the distorting effect of the prism
being then simply employed in rendering straight the slit-images
which form the spectrum.
I think it just worth while to mention, in corroboration of
Mr. Gkubb's paper, that the same sufficiently obvious remedy
oceurred to me some time ago, and that since November last I
have had curved slits in use for a lantern-spectroscope with per-
fectly satisfactory results. These are screwed on (in front of)
the ordinary slit-plates, which latter are opened wide ; and the
curved plates are thus readily replaced by others by loosening a
couple of milled-head screws. Any spectroscope may in this
way have the additional slit-plates fitted to it with very little
difficulty or expense.
I have two pairs of slit-plates with curved edges thus fitted to
my original slit : — one with edges curved to a radius of 21 cen-
tims., which sensibly corrects the distortion of a single carbon-
disulphide prism, the refracting angle of which is 60^ ; the other
slit has a radius of curvature of 10 ccntims., and is used with a
train of two similar prisms. In using such slits with a conden-
^ug-lens between them and the prism, they should be so placed
that the centre of curvature is on the side towards which the
rays are refracted by the prism. The above curvatures were de-
termined empirically by trials with tinfoil slits, which were easily
made by attaching a piece of tinfoil to a plate of glass with gum,
and (before the gum was dry) cutting out very narrow strips by
a knife fixed to one leg of a pair of beam-compasses. In this
way a number of trial slits may be made and tested ; and when
the curvature of that one which performs best is noted, any
good optician will make a pair of brass plates with edges of the
proper form.
I remain,
Yours faithfully,
H. G, Madan.
Eton College. July 18, 18/4.
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[ 117 ]
XX. On the General Theory of Duplex Telegraphy.
By Louis Schwendler*
Introduction.
rpHE name of "duplex telegraphy '^ has been given to that
-»- node of electric telegraphy which admits of the simulta-
neous transmission in opposite directions of signals between two
stations through a single wire. That this name is far from
happily chosen is evident ; but as it is current and has aJready
gained a recognized footing, it is not considered advisable to en-
deavour to replace it now by a more rational one, and it will
therefore be adhered to throughout this paperf.
In the following investigation I shall endeavour to develop
the mathematical theory of *' duplex telegraphy *' in its most
general form, with the object of determining not only the best
arrangement for any particular method, but also the relative
values of different methods.
It is manifest that, having from general considerations decided
on the best method, and further determined the best arrange*
roent for this method, the remaining diflSculties, due to the
nature of the problem itself, will be exhibited in a clearer light,
and the means of overcoming them may then be more easily
discerned.
It is believed, however, that the sequel will show that, if the
best method be adopted, and for this method the best arrange-
ment be selected to suit the particular line on which the method
is to be employed, the difficulties that stand in the way of duplex
telegraphy will hardly be greater than those which are encoun-
tered every day in ordinary single telegraphy.
Imperfect Historical Sketch.
Having access to but scanty records in this country, I am
not in a position to give an exhaustive' history of this most im-
portant invention ; and consequently the following sketch is ne-
cessarily incomplete, and must be taken as merely introductory,
it being relegated to those better situated in this respect than
myself to clear up the doubtful points of priority, and produce,
what is much required, a complete history.
The idea of sending signals in opposite directions simulta*
neously through a single wire is by no means a new one. As
* From the ' Jounial of the Asiatic Society of Beagm]/ vol. xliii. pt. 2,
1874> having been read before the Society on the 4th of February, 1874.
Communicated by the Author.
t The German language potsesses a peculiarly suitable word in "Oegert'
sprecheH;'* and the idea is fully rendered by ** glekhzeitige$ Gegen-»
sprtchen"
Digitized by VjOOQ IC
118 Mr. L. Schwendler on the General Theory
early as 1849 Messrs. Siemens and Halskej of Berlin^ took out a
patent in England^ for the simultaneous transmission of a plu-
rality of messages' by a suitable combination of wires; and
although this patent does not refer directly to duplex telegraphy
as it was subsequently understood, it must^ notwithstanding^
be regarded as a forerunner of it. In point of fact. Dr. W.
Siemens'! idea represents the general problem of which duplex
telegraphy is only a particular case.
In 1854 Dr. Gintl^ of Vienna, tried his ''compensation'^
method of " duplex" working between that capital and Prague fj
and on the 30th November of the same year read a paper before
the Kaiserlich-konigliche Academic of Sciences of Vienna ^ on
the practical solution of the same problem by employing a Bain's
electrochemical telegraph-apparatus instead of a Morse's receiv*
ing instrument.
In the summer of 1854, after Dr. Gintl's experiments be-
tween Vienna and Prague had brought the subject prominently
to notice, Messrs. Siemens and Halske, of Berlin, and Herr
Frischen independently^ invented the " differential " method.
In January 1855 Edlund§ made experiments oh the line be*
tween Stockholm and Gothenburg. He employed a ''differen*
iial " method, which he had invented in 1848, for the purpose
of measuring accurately Faraday's *' extra currents."
In papers read at Paris on the I6th July and 6th Aug^t,
1855 II, before the Academy of Sciences by M. Zantedeschi, he
claims the honour of having first suggested the idea of duplex
telegraphy ; for as early as 1829 he had proved the possibility
of the simultaneous transmission of currents in opposite direc-
tions through a single conductor. Having never seen his ori-
ginal communication of 1829, it is impossible for me to say how
far these early ideas of Zantedeschi bear on the problem ; but it
is certain that both he and Dr. Gintl took a great deal of trouble
to prove an erroneous theory, viz. that two distinct electrical
currents can pass simultaneously in opposite directions through
the same conductor without in any way interfering with each
other. Such a supposition is in direct opposition to the elec-
trical laws which were already known in 18291, and besides
is in no way required in order to explain the simple pheno-
nienon of duplex telegraphy**.
* 23rd October, 1849. The actual wording of the English patent is
unknown to me.
t Polyt. Centralbl 1863, p. 1476.
X Wien, Akad, Sittungsber, zir.
§ Pogg. Ann. 1856, vol. xcviii. p. 634. H Ibid. p. 123.
' 'If Ohm published hisclatticfll work Die siakanische Kette mathemati$ck
bearbeitet in the year 1828.
•♦ I>r. W. Siemens, Pogg. Ann, vol. xcviii. p. 123,
Digitized by VjOOQ IC
qf Duplex TeUgrc^hy. 119
* None of the above methodd^ however, came to have ex-
tended, or indeed any, practical application. They appear to
have been attempted doabUngly and without confidence; and
although the trials are generally reported to have been bug-
eeasful, yet the methods were rejected aa impracticable, and
came to be regarded aa merely of scientific interest 'i'.
Only recently, after a torpid existence of almost twenty
Tears, has duplex telegraphy been revived, and come to be the
leading topic in telegraphy, securing after such a lapse of
time the amount of public interest it rightly deserves.
To Mr. Stearns, an American telegraph-engineer, is due
the honour of having appreciated the real value of duplex tele«
graphy, and of having (by giving the system, modifiecl by im**
provements of his own, an extended application on the lines of
the United States) proved its thorough practicability.
Inquiry into the Caiues which have delayed the introduction of
the System.
When Steinheil in 1837 announced his discovery of the feasi-
bility of employing the earth to complete the electric circuit in-
stead of a return-wire, telegraph-engineers immediately recog-
nised its immense mercantile value, and did not delay to verify
his results.
Now, in the career of telegraphy, the invention of duplex work-
ing ranks second only in importance to SteinheiPs discovery.
The utilization of the earth reduced by one half the number of
wires required to carry a given traflSc : duplex telegraphy again
almost halves this number. In the face of this fact it is not easy
to understand why the one idea received immediate and universal
application, while the other, of only about ten years more recent
date, has met, until now, with universal neglect ; but on closer
examination it will be found that there have been perfectly com-
prehensible, although not all rational, infiuences at work.
An inquiry into the circumstances, therefore, that have caused
ihe discovery of a system, the introduction of which must mark
the second great era in telegraphy, to lie fallow for nearly twenty
years is of the utmost interest, and cannot fail to be instructive
with regard to the prospects of future progress.
From an examination of the methods originally proposed for
duplex working, it will be found that they do not in any way
essentially dififer from those which may now come into actual
use. The causes, therefore, which have prevented the intro-
duction of the system must be sought for external to the
methods.
. * For the light in which daplex tdegraphv was regarded till quite lately,
see SchellcD, Dab, Sabine, Blarier, Kuho, &c.
Digitized by VjOOQ IC
120 Mr. L. Schwendler on the General Theory
The fir&t of these^ we find> is that the invention was in ad-
vance of the requirements of the age. Telegraph-lines had
already been constmcted which were quite capable of carrying
the given traffic and even more. Further^ any increase in traffic
could be easily met by an increase in the number of wires on the
existing telegraph-posts^ instead of by resorting to a system which
had a complex appearance^ and after all might not answer.
However^ although the above considerations explain the course
of events in certain limited instances^ and up to a certain time^
they do nothing towards justifying the costly expedients that
have been generally adopted until recently in preference to in-
troducing duplex telegraphy — for instance, the reconstruction
and multiplying of long overland lines^ and especially the laying
of a second submarine cable when the traffic became too great
for one.
• It is time that the successful application of any duplex me^^
thod requires lines of a more constant electrical condition, re-
ceiving-instruments of a larger range*, and telegraph-operators
of a somewhat better professional education ; but surely these
three conditions have not all at once become fulfilled (since 1872)|
so as to make duplex telegraphy possible only just now f No;
the causes which have delayed its introduction so long have
been of a much less technical and more irrational nature*
The mere fact of the duplex methods appearing complex pre-
vented telegraph-administrations from thinking seriously of in-
troducing them. The ingenious methods were never tried with
that zeal and perseverance which is necessary to carry a new
invention successfully through. They were indiscriminately
Injected after a few trials made without method or considera-
tion ; and the real conditions of success or failure were never
examined or pointed out. Thus naturally a prejudice was
created against duplex telegraphy, and it was fostered by a
host of school literature up to the latest time, as pointed out
before. Further, not a single physicist or electrician investi-
gated the question with a view to ascertaining what quanti-
tative effect the variable condition of lines has on duplex work-
ing as compared with single working.
If such an investigation had been made, it would have been
found that the technical obstructions in the way were by no
means so formidable as had been represented, and that the
• By the " reuge " of a telegraph-instniment I undcrstnnd the ratio of
the largest to the smallest force by which the instrument in question can
be worked without requiring a fresh mechanical adjustment, ror instance,
Siemens's beautiful relays can be easily adjusted to a range of 20 ; i. e.
they can be made to work with one cell through an external resistance
equal to their own resistance, and w ith ten cells tlirough no external resist-
ance, without giving the tongue a fresh adjustment.
Digitized by VjOOQ IC
ofDt^lex Telegraphy. 121
electrical condition of the lines^ as well as the perfection of the
instraments and the professional education of the staffs would
have fully admitted of the successful introduction of duplex
telegraphy at least ten^ if not twenty, years ago.
It is true indeed that the suggestion of using condensers for
balancing the charge and discharge of a line has only been made
very lately, being one of Stearns's happy ideas ; but this should
have been no reason against introducing the system on short
and overworked lines, where the charge and discharge is imper*
ceptible. If only one telegraph -administration had shown the
perfect practicability of the system on a short line, the cloud
of prejudice would have been dissipated, and suggestions for
overcoming the charge and discharge on long overland lines
and submarine cables would have been readily enough given,
and thereby large capitals saved.
To sum up, therefore, we have the following causes which
acted persistently against the introduction of duplex telegraphy^
First, the invention was in advance of the age.
. Secondly, the telegraph profession, young as it is, is far more
conservative than is good for the advance of telegraphy ; and,
on the whole, telegraph-administrations and staffs have by no
means that professional education which is required to conduct
practical experiments with a clear understanding, and thence
deduce rational conclusions. Thus prejudice was created, which
was increased from year to year by authors of school literature
writing most discouragingly on the subject.
Thirdlv, unfortunately during all that time no physicist found
it worth his while to investigate the duplex methods with a view
to ascertain quantitatively what can be expected of them, and
how they actually compare, with respect to safety, with single
working.
Fourthly, duplex working itself could not progress, because
it was neither tried nor investigated, and hence no sugges--!
tions for overcoming the difficulty of charge and discharge
were called for.
Great honour must therefore be given to Mr. Stearns, who
brought up the subject again so prominently, and who by his
zeal succeeded in introducing it on a large scale, and so elevated
the ingenious methods from the questionable position of '^ inter-
esting scientific exi>eriments.''
I think far less of his idea of introducing condensers or
Ruhmkorff's coils to balance the charge and discharge of lines>
than of his having taken the neglected child up again against
the prejudice of his own profession, and shown that it could
have a healthy existence even in the backwoods of Ameriea*
I trust that these remarks will not be considered irrelevant in
Digitized by VjOOQ IC
I2i Mr. L. Schwandler on the General Theoty
the present iDvestigition, siDce they tend to show how real
Erogress in one of the youngest branches of applied seienoe may
e retarded for a considerable period by nothing bat prejudice
of the profession themselres^ for whom the progress should be
the first essential ; and administrations will see how much the
advance of telegraphy will always depend on their recognising
and encouraging by experiment inventions that are theoretically
sound and tend in the right direction.
General Consideratiane.
Before entering on the solution of the problem for any par-
ticular duplex method, it would be advisable once for all to
state definitely the nature of the general question before us.
This will not only save time, but the subsequent special 8olu«
tions can then also be made under a general guide ; and thus,
being well linked together, the whole investigation will become
£ir more lucid and concise than it otherwise would be.
While in ordinary (single) telegraphy the signals are always
produced in the same way, t. e. by the signalling current arri-
ving through the line from the distant station, the signals in
duplex telegraphy may be produced in either of two ways essen-
tially different from each other. Namely, if the times of slid-
ing from the two stations fall together, t. e, no current, or
double current, or any difference of currents is in the line, the
signals, so long as this state of the line exists, are produced
wholly or partly by the battery of the receiving-station. Sig-
nals produced m this way we shall call ^* duplex signals ;" and
these signals alone indicate the essential difference between
duplex and ordinary telegraphy.
If, however, the moments of sending from the two stations
do not fall together, the signals are then produced as in ordi-
nary telegraphy, and may be appropriately designated ^* single
signals.'^
It will be clear, then, that when the two stations are at work
at the same time, " duplex signals '* and " single signals ^' must
necessarilv follow each other in accidental succession. Nay,
one and the same signal produced in either station may be partly
a ^'duplex '^ and partly a '' single^' signal.
To secure, therefore, regularity of working, the signals pro-
duced in either way should be invariably of equal strength.
Further, as in duplex telegraphy the receiving-instruments
must be always permanently connected up with the line, it is
one of the first reauirements that the out-going or sent current
from any station snould in itself have no effect whatever on the
reeeiving-instrument of that station, in order that the instru-
ment may be entirely fr^ \g r^y^ ^gnals from the disunt
Digitized by VjOOQIC
of Duplex Telegraph}f. 123
sUtioii, Thus we invariably have two conditions to fnlfil in
duplex workings independent of the particular method adopted,
namely :i — .
1. The reeewmg-ingtrument of each station ihouldnot be affected
by its own sending.
2. Tlie duplex signak and single signals must be of equal
strength.
If these two conditions, which are necessary and sufficient,
eould be always fulfilled, duplex telegraphy would be entirely
on a par with single telegraphy ; for the sending would not only
not interfere with the receiving (the more important condition of
the two), but the received signals would also be constant in
strength, and therefore frequent adjustment of the receiving-
instrument would be no more required than in single telegraphy.
Theoreticallv, of course, every duplex method hitherto sue*
gested fulfils these two conditions; otherwise the method would
have to be rejected a priori, and could not find any place in this
paper.
Practically, however, the different methods may behave very
differently with respect to the fulfilment of these two conditions ;
nay, even one and the same method is sure to give quite different
results in this respect by only altering the magnitude of the
resistances of which the arrangement consists. For in practice
variations, especially in virtue of the line having by no means a
constant electrical condition, are necessarily going on. These
unavoidable variations, it is clear, may cause very diffei*ent quan-
titative disturbances of the two conditions (1) and (2), either if
we compare different methods, or the same method under differ-
ent resistance arrangements.
To make the foregoing clear, we will designate : —
by p the force which acts on the receiving-instrument on
account of not being able to fulfil the first condition absolutclv ;
by P the force which acts on the same instrument when the
distant station is sending alone, i. e. ^' single sisals;''
and by Q the force which acts on the same instrument when
both stations are sending simuUaneouslg, i. e. ** duplex signals.'^
. Then the first condition (1) is expre^ed by
p-o, (I.)
and the second (2) by
P-Q«0. (II.)
Further, if p cannot be always kept rigidly equal to zero (on
account of unavoidable variations in the system), we should at
leadt have
£-&sD as small as possible; • . • • (III.)
Digitized by VjOOQ IC
124 Mr. L. Schweudler on the General Theory
and if P cannot be always kept rigidly equal to Q, we should at
least have
P^QsbS as small ^ possible^ • . . (IV.)
p, V, and Q being functions of the resistances and electromo-
tive forces of the system^ which are known so soon as the parti-
cular duplex method has been selected.
The general problem which is to be solved for duplex tele-
graphy may now be clearly stated as follows : —
I) and S are two known Junctions which must be rigidly equal
to zero when no variation in the system occurs, and which for any
given variation in the system must be as small as possible, and ap^
proximate rapidly towards zero as the variation in the system
becomes smaller and smaller.
Thus the solution of the problem for any civen duplex method
will always be a question of the minima and maxima calculus.
Having then ascertained the best arrangement for each duplex
method^ the methods can be compared inter se; and that method
will be best^ and should be selected for use^ which for any given
variation in the system gives the least absolute magnitude to the
functions D and S.
If we suppose, however, that the particular duplex method is
not given, the problem to be solved becomes more general, but
would still be entirely within the limits of the variation cal«
cuius, furnishing, no doubt, a very interesting and important
application of that most powerful mathematical instrument.
The general solution would at once determine the best method
possible, after which special solutions would give the best ar-
i^ngemcnt for that best method.
It is, however, not my intention to endeavour to solve here
the duplex problem in this most general form. To be able to
indicate so general and desirable a solution is by no means
identical with being able to effect it. The task before me is ht
more simple, since, as already pointed out, I shall investigate
each duplex method separately to determine its best quantitative
arrangement, and ultimately compare the different methods to
ascertain their relative values.
To do this, the question may be attacked in two different
ways, . depending on . the purpose for which the solution is
required.
Namely, either the solution is to be made when considering
the line as a variable conductor only, but not acting perceptibly
as a Leyden jar ; or the line is to be considered as constant in
conduction and insulation, but acting as a Leyden jar of large
capacity. In the first case the solution would be directly appli-
tMt to short overland lines (not over 200 miles in length), and
in the second case to submarine cables, which, if good, may
Digitized by VjOOQ IC
of Duplex Telegraphy, 125
always be considered sensibly constant in conduction and in-
sulation.
Further^ as a long overland line acts both as a variable con-
ductor and as a Leyden jar of sufficiently large capacitv^ it would
then be necessary to give a solution with respect to both these
effects. To obtain^ however^ the same result without rendering
the problem too intricate, it will be best to separate the two
questions from the beginning, and afterwards combine their
solutions judiciously for application to the case of overland
lines.
1st Problem. What is the best arrangement of any given duplex
method when the line is regarded as a variable conductor^ but not
as acting perceptibly as a Leyden jar?
2nd Paoblem. What is the best arrangement of any given duplex
method when the line is regarded as a Leyden Jar of large capacity,
but not as a variable conductor.
The second problem may be expressed more clearly as fol-
lows:—
2nd Problem. What must be the distribution of condensers
along a given resistance, in order that the two essential conditions
(I. and II.) may be least disturbed for a speed of signalling variable
between two fixed limits ? *
* A tele|^raph-liDe always acts as a condenser with capacity and con-
duction-resistance in each point of its entire length, while an artificial
condenser (such as a Leyden jar) which we are ahle to produce sufficiently
cheaply has only capacity but no perceptible conduction-resistance in each
point. This is in fact the essentud difference between a line and a con-
denser; and therefore, in order to render their charges and discharges
under the same circumstances as nearly as possible equal, as is required
for duplex working, it will be necessary to find the law according to which
to distribute a certain given system of condensers along a given re-
sistance.
This law will clearly be a function of the signalling speed within its
limits of variation. For instance, say the signalling sp^d is constant, or
its range zero, then clearly one condenser connected to any point of the
given resistance would suffice ; only the magnitude of the capacity of this
one condenser would be determined bv its position with respect to the re-
sistance, and, in addition to this, would of course be fixed by the signalling
speed and the known capacity of the line.
Further, say the speed of signalling is variable betwen 0 and oo , or its
range is infinite, then clearly only an infinite number of small condensers
distributed alon^ the given resistance in the very same manner as the
capacity is distributed dong the line would strictly answer the purpose ;
in £ACt, the condenser required in this imaginary case would be nothing
more or less than a second telegraph-line, identical with the one used for
signalling. In practice, however, the speed of signalling varies only be-
tween narrow limits ; and therefore the number of condensers required to
reproduce as nearly as possible the action of the line with respect to charge
and discharge, will become few, especially if the best system of distribu-
tion has been determined. Until this law is known, we can do nothing
Digitized by VjOOQ IC
126 Mr. L. Schwendler on the General Theory
It U clear that the natare of these two problemg ia very
different, because in the first we have to deal with forces con-
stant with respect to time, while in the second the forces acting
are functions of time, i. e. of the signalling speed. (The fwces
in this case are proportioned to the true currents.) The latter
problem being far the more intricate, and for my special purpose
only of secondary importance, I shall begin with the solution of
the first.
Solution of the first Problem for my given Duplex Method,
What is the best arrangement of any given duplex method when
the line is regarded as a variable conductor ^ but not as acting per'-
ceptibly as a Leydenjarf
I. The bridge method*.
This arrangement for duplex working is based on the well*
known method of comparing electrical resistances, 'MVheat-*
stone^s bridge ;'' and the figure (p. 127) gives the general dia-
gram when this method is applied for duplex working.
/9 is the internal resistance of the signalling. battery.
1/ the ^'measured conductor ^^f resistance of the line when
measured from station I. ;
but find it spproximately by experiment, however tedious it may be t«
dose.
It has also been proposed to use Ruhmkorff's coils for balancing the
effect of charge ana discharge. This method, however, I l>elieve must be
always much inferior to the one of using condensers, inasmuch as the
strength of a voltaic induction-current scarcely depends on the speed of
signalling, while the charge and discharge of a line, it is well known, is
not at all an inconsiderable function of the signalling speed.
Therefore if the strength of the induction-current had been a4insted to
balance the charge and discharge of the line for a certain signalling speed*
the balance would be considerably and at once disturbed if tbs speed
varied even slightly; and since so long as hand signalling is used a certain
variation in the speed of signalling wiU always exist, this method will prove
a fisilure, or at afi events will render fresh adjustments more frequently
necessary than when condensers are used.
* Dr. W. Siemens mentions this in Pogg. Ann, vol. xcviii. p. 122 (1866).
Mr. O. Heaviside (Phil. Mag. 1873, voL xlv.) sUtes that Mr. Eden, of
Edinburgh, claims to have suggested this method at about the same time
as Mr. Steams, of Boston, U.b.A., took out a patent for it.
t Genendly these measured values U and L" will be different from each
other, especially for lon^ overland lines. They can become equal only
under two conditions— either if the resistance of the resultant fault (t) is so
great that the total conductor resistance of the line (/'-|-r'as/} can be nej^*
lected against it, or for any magnitude of t if the latter has a position m
the middle of the conductor, t. e. when Ts/^a^*
Digitized by VjOOQ IC
of Duplex Telegraphy. 127
JP the '' measured conductor '' resistance of the line when
measured from station II i
•••"=''+ i^-
(f the complex resistance of the duplet arrangement in station
I.^ t. e. the resistance between point 1 and earth.
fff the complex resistance of the duplex arrangement in sta-
tion 11.4 1. e. the resistance between point 2 and earth.
£^ electromotive force of the signalling-battery.
ffy the resistance of the receiving-instrument.
K, telegraph-ke]^ of peculiar constniction^ to be described hereafter.
g, the receiving-instrument eonnccted up in that branch of the bridge
which, when measuring resistances, would contain the galvanometer*.
a, b, and d are the branches of the bridge.
/, the resistance between the rest-contact of the key and earth.
w, an additional resistance to be inserted in the battery-branch, for rea-
sons to be ^ven further on.
t, the resistance of the resultant fault {" real absolute insulation " of the
line) acting at a distance /' from station I. and at a distance f from sta-
tion II. (both /' and T expressed in resistances so that f+r=sl equal the
" real conductor resistance " of the hue).
To be quite general^ we must suppose that the telegraph-line
which connects the two stations I. and II. has a different resist-
ance when measured from station I. than when measured from
station 11.^ and that therefore the best resistance-arrangement
of station I. must be also different from that of station II. with
respect to magnitude of resistances.
* Siemens's polarized relays are well adapted for this purpose, on account
of their great sensitiveness and wide range ; D* Arlincourt's relays would
also answer well. .
Digitized by VjOOQ IC
128 Mr. L. Schwcndler on the General Theory
The resistances which are similarly sitoated in both the sta-
tions will be designated by the same letters ; and to indicate the
station to which they belongs each letter will have one accent in
station I. and two accents in station II.
Further^ if a relatioa between the resistances of one station
has to hold good between those of the other station also^ the let-
ters will be used without any accents.
The great practical advantage of the bridge method, it will be
clear at once^ is that any kind of receiving-instrument which has
been used for single working may also be employed for duplex
telegraphy. This fact must always be of great consideration for
any administration that contemplates the general introduction
of duplex telegraphy.
General esfpressions for the two functiom D and S.
To obtain the functions D and S^ we have first to develop the
general expressions for the forces /»^ P, and.Q> say for station I.
By j/ we understand the force which acts on the receiving*
instrument g^ of station I. when that station is sending alone
(station II. at rest).
y, in our particular case, is therefore proportional to the cur-
rent which passes through the galvanometer in a Wheatstone^s
bridge when balance is not rigidly established ; thus
where
and
N'=y(i' + dO(«' + c') +/{y(a' f i' + c' + rf') + (^+rf')(«' + iO }
Further, by P' is understood the force which acts on the re-
ceiving-instrument in station I. when station II. is SLnding
alone : single signals.
This force in our particular case is proportional to the current
which passes through the receiving-instrument of station I. when
station II. is sending alone ; and we have consequently
where C" is the current which enters the line at point 2 when
station II. alone is sending, C"/jJ the part of this current C"
which arrives actually at point 1 (on account of leakage between
points 2 and 1, a part of C is lost), and CV'V^ ^hat part of the
current C"/J which ultimatelv produces the signal {sirigle signal)
in station I. The current CV' arriving at point 1 branches off
Digitized by VjOOQ IC
of Duplex Telei/raphtf. 129
ia two ; one part goes through a* and the other through ^ to
earth.
Farther, n»_w »»"
C»«E»
w
where
FocE"^,m'i^;
m!^
t
and N" an expression identical in form with N'.
Farther^ by Ql we understand the force which acts on the
receiying-instrument of station I. when both stations are send*
ing simoItaneoQsIy : duplex signals.
This force is again proportional to the current which, under
these circumstances, passes through the receiving- instrument ^
of station I.
This current can be expressed by
and therefore
a* being the current actually in the line at point I when both
stations are sending simultaneously ; and this current, being the
algebraical sum of two currents, may be either +, 0, or — .
We will suppose that <r' contains the sign itself.
Further, we have
, EW E'W ,
and ^ is a function which becomes identical with '^' if we put
Therefore the two functions D and S are for the bridge me-
thod (station I.) most generally expressed as follows : —
E'N" 1 A' ,„„.
Phil. May. S. 4. Vol. 48. No. 316. Aug. 1874. K
Digitized by VjOOQIC
ISO Mr. L. Schwendler on the General Theory
and
s'^E'^/.y-^+o'^'j . . (IV.)
and similar expressioDs will be obtained for station II., namely
and
S''-F^M''^-^f+^^. . . (IV".)
Bigid fulfilment of the first condition, L e. D=0«
For statton I. we have
which equation can only be satisfied by
since the other factor of D' cannot become sero for quantities
larger than 0 or smaller than oo. Then, substituting for A' its
value^ we have
a'd'-4'(L'+/)=0; (V.)
or balance in station I.^ when that station is sending and sta-
tion II. is at rest, must be rigidly established.
Therefore if balance in station I. is disturbed, say by 1/ vary-
ing or by any other cause* external to U, we most have means
of conveniently reestablishing balance without delay. This, of
course, could always be done by altering either all the branches
of, V, and d!, or any two of them, or only one of them ; but it
is clear that so long as the variation of V which disturbs the
balance does not exceed certain limits, balance may be regained
by altering only one of the three branches available ; and as this
will also be more convenient in practice than altering two of the
branches, or all three simultaneously, we shall make the suppo*
sition that
" Balance is reestablished by an appropriate readjustment of one
of the three available branches" f.
* Causes of disturbance to balance external to L' are inappreciable in
practice and therefore may be neglected from the beginning.
t Finally, when the hest resistance-arrangement has been found, the
resistance of the different branches will be expressed in terms of L ; and
therefore to keep the best arrangement when L varies between any two
given limits will involve necessarily a simultaneous alteration of the resist-
ance of all the branches.
If, however, the variation of L is small in eorapnrison with L itself, an
alteration of one branch for the purpose of reestablishing balance is justified,
and would be absolutely correct if the variation of L \\erc iufinitesimal.
Digitized by VjOOQ IC
of Duplex Telegrophy^ 131
The question therefore is^ which of the three branches^ a, b,
or d, is the best adapted for the purpose?
To decide this we must remember that for station 11.^ in ac-
cordance with the first condition (DsO)| a similar equation has
to be fulfiHed, namely^
fl"J"-J"(LW+p')«0. .... (V.)
Now o'^ the complex resistance of the arrangement in station
I., is a function of all the resistances in station I. ; and similarly
pf, the complex resistance of the arrangement in station 11.^ is
a function of all the resistances in station II. Therefore^ gene-
rally, if in order to obtain balance, say in station I., any of the
three branches of, V, tP were adjustecC ff would alter in conse-
quence of this readjustment, and thereby the balance in station
II. (equation Y".) would be disturbed, and vice ver$d. In other
words, the readjusting in one station would interfipre with the
balance in the other station, and therefore rigid balance could
be only attained after a series of successive adjustments in both
the stations — and then only, from a theoretical point of view,
approximately, introducing practical difficulties almost insur-
mountable.
However, examining the positions of the three branches, it
will be seen at once that b acts as the galvanometer-branch of a
bridge for any current arriving through the line. Thus, if we
were to fulfil the condition
ad^fff^O (VI.)
for both stations, the value of p would become at once indepen-
dent of b^, and consequently any adjustment of V to reestablish
balance in station I. would not affect in the slightest degree the
balance in station II., and vice versd.
Thus, presupposing the fulfilment of this condition (equa-
tion VI.) for both the stations, the branch b would evidently be
the best suited for adiustmentf. Under these circumstances it
would then be clear that balance in either station can be obtained
by a smgk adjustment of b ; and therefore we mav call equation
VI. ** the immediate-balance condition ;^' and the fulfilment of this
condition being of the greatest practical importance to ensure
the success of duplex working, we are justified, nay even com-
* ^,(y+^)(«+/)_(arf~/y)«
Therefore if ad—fg is very near sero» p becomes most rapidly indepen-
dent Of b.
t Farther, it mutt be remarked that, even if the condition ad—fg^O be
not rif^dly fulfilled, still 1^ adjusting in the branch b we have '* aecele*
rated" balance, whereas by adjusting in a or d we should, on the contrary,
We "retarded'* balance.
K2
Digitized by VjOOQ IC
132 Mr. L. Schwendler on the General Theory
pelled, to use this relation (equation VI.) as the basis for all
subsequent investigations.
We will therefore suppose henceforth that
ad^fg^O (VI.)
is rigidly fulfilled for both the stations.
But as the value of / depends on the position of the key,
which during signalling moves from contact 3 to contact 4 and
back, the rigid fulfilment of equation (VI.) necessitates at once
that
u;+i9=/, (VU.)
not only for both the contacts 3 and 4, but also for all the in-
termediate positions of the key. Thus, supposing that u^ + ^ »/>
t. e. the resistance from contact 4 through battery to earth equal
to the resistance from contact 3 to earth, a key constructed in
such a way that contact 4 is not broken before contact 8 is made,
and that contact 8 is not broken before contact 4 is made, would
fulfil the required condition entirely. Keys of this kind can be
easily enough constructed. It is true that in any such key there
will be alwavs a moment when the contacts 3 and 4 are simul-
taneous, and when therefore the resistance to earth is not /, as
f
it ought to be, but only ^. Considering, however, that the time
during which this error lasts is very small compared with the
time it takes to make a signal, its disturbing effect will never
be appreciable in practice ; t. e. p will remain sensibly constant
during the time the key is moved to produce a signal.
There will be no practical difficulties connected with the ful-
filment of equation (VII.), and therefore also none with the ful-
filment of equation (VI.) ; for 0, the internal resistance of the
signalling-battery is the only Quantity which of itself can alter
in time. However, this variation of fi for any efficient form of
signalling-battery being invariably steady and small, it will be
always possible to neutralize its action in time by a simple read-
justment of w.
If Leclanch^'s cells are used, or well prepared Minotti's, a
weekly adjustment of w should be sufficient. The measuring
of ^8 will always be an easy matter*.
* My friend Mr. R. S. Brough suggested the following very simple me-
thod for keeping
«^+/3=/. (VII.)
Insert a small galvanoscope in the branch b, for which balance is estab-
lished with res|)ect to the received current, t. e.
ad^fff^O (VI.)
Now note the deflection on the galvanoscope when both stations are
Digitized by VjOOQ IC
of Duplex Telegraphy. ) 38
Rigid fulfilment of the second condition^ i, e. SsCX
The general expression for S' was
S'=-j^Kr — ;f+^i>'^ • • • (IV.)
Bememberingthat by equation (VII,)
we know that V^=<^; and substituting further for a' its value,
the general expression for S' becomes
S'--jprA*y— ^+ |-^--j^-^/|v^; (m)
and this form of S' shows at once that it is perfectly immaterial
for duplex working by the bridge method whether the same or
opposite poles of the two signalling-batteries be put to line^; for
in both cases equation (IV.) becomes
S'=^V^-B'^ (IV.)
Further, it will be seen that the right-hand member of eqna-
A'
tion (I v.) can be transformed f into E'm, which is equal to//,
or we have generally
S^p;
i. e. the difference offerees by which duplex and single signals in
sending timultaneonslv, snd agsin when the station for which /3 is to be
measured is sendinr alone. Then dearlv, if these two deflections are equal,
ID+/S must be equal to/. If the two deflections are not eoualy then alter
w until they hecome equal. After the determination is maae the galvano-
scope is short-circuited.
* In practice, however, I prefer to put the same (namely the positive)
poles to the line, as then defective insulation will not be felt so much.
t We have
j^^mifc— All
S=
b '
mAr—Afi
EbA
Digitized by VjOOQ IC
184 Mr. L. Schwendler on the General Theory
the same station are produced is equal m magnitude and sign to
the force by which balance in that station is disturbed.
Consequently the rigid fulfilment of the fint condition (DbO)
will entail the rigid fulfilment of the second condition (S=0) ;
and this, it will be clear, is only due to the fact that the complex
resistance p is independent of b, and that the key during signal-
ling does not alter p ; whence it follows that the perfection of
the key in this respect is of the greatest importance. There are,
however, no practical difficulties connected with the construction
of a key which fulfils condition (VII.) perfectly.
By the aid of the relations giren in equations (VI.) and (VII.)
we have therefore gained the*great practical advantage that du-
plex telegraphy will be entirely on a par with single telegraphy,
if the means of attaining rigid balance are sufficiently accurate,
eoavenient, and rapid.
But, even sunposing that we are unable to keep that balance
rigidly for any length of time (on account of L varying), we can
nevertheless bring the regularity of duplex working as near as
possible to that of single working by making D and S as small
as possible. foe any given variation of L«
Rapid approsimatian of the twofunetions D and S towards i$ro.
For station I. we had
s'=y«^^-^, . . . . OV.)
which we may also write
since
and
Further, if we call V the value of b which in station L esta-
blishes rigid balance for any given values a', d', and 1/, we have
A'=4'.SI/,
where SV is the variation of L' which throws the balance out,
and which variation may be either positive, eero, or negative
(SL' shall contain the sign in itself).
Digitized by VjOOQ IC
of Duplex Telegrt^ky. 135
Further, substituting
and
•^'^
rt '
the expression for S' may be written as foUovs : —
8'»yocG
1 ,
^-y
zQ/¥',
which is the best form of S' for our purpose.
The function S' consists of two factors — namelyi of C, which
at or near balance is proportional to the current by which duplex
and single signals in station I. are produced, and of V, which
at balance ssO.
Therefore to make S' as small as possible when balance is
disturbed, we can only do so by making F as small as possible,
which is evidently the case for y's: -^ a maximum. Further,
S'-Q'F';
and since at or near balance
FaG',
it follows that j)/^ p .
t. e. the first eondition is also fulfilled by
y'ss -^ a maximum.
Our problem for station I. would therefore be most generally
solved if we make the function ^ a maximum, remembering that
the variables contained in y' have to fulfil two condition equa-
tions, namely the immediate balance (equation YI.) and the ba*
lance (equation Y.).
Substituting for m' its value, and remembering that
on account of the immeiiaie-balance condition (equation IV.), we
get
Digitized by VjOOQ IC
136 Mr. L. Scbwendler on the General Theory
But
the complex resistance of station I. (the expression for p has be«
come thus simple on account of the immediate-balance condition
VI.).
Further,
(on account of balance in station I. being established^ equationV.).
Thus we have
y' = p' + p"+I/
for station L ; and similarly
for station II.
Therefore the rapid approximation of both the functions D and
S towards zero in both stations is obtained \f we make the complex
resistances p! and p" maxima.
Now the form of p shows at once that it has a maximum for
• (fl+/)=(y+rf),
which, in consequence of equation (VI.)> gives at last
«=^=rf=/. (VIII.)
From the development of this result it will be clear that the
relation expressed by equation (VIII.) must hold for either.
station independent of L.
All that now remains is to determine b, and further to fix the
absolute magnitude of any one of the branches. Before doing
this, however, it is necessary to inquire what the other factor of
8, namely G, becomes in consequence of fulfilling the regularity
condition as expressed by equation (VIII.).
The current which passes through the receiving-instrument
to produce ''single'* as well as "duplex'' signals is at balance
expressed by
^=^ • 7 — . MT / — . N . o / — rifv; X const.,
(a+y){L(a+y)+2%+rf)} '
which expression has a maximum for either a or g.
The maximum of G with respect to a, it will be seen, contra-
dicts the regularity condition, since a=^g^d could only satisfy
da
if d were negative, a physical impossibility.
Digitized by VjOOQ IC
of Duplex Telegraphy. 187
However^ the maximum of G with respect to g gives
which is satisfied by a^g^d.
This is a fortunate coincidence, and speaks well for the bridge
method.
Now substituting for a and d their value g in the expression
for the current G, we get
n E 1
and this expression multiplied by ^g gives the magnetic effect
of the receiving-instrument, namely
which has an absolute maximam with respect to g for
L
Ftrrtfaer, substituting in the balance-equation (V.)
a = d=g=r^,
^'-'' ft=| (IX.)
Wc have therefore the following two equations by which the
problem is generally solved : —
a^g=d^f=\, (VIII.)
*=i = B m
by L being understood the measured conductor resistance of the
line from that station for which the best resistance -arrange-
ment is to be calculated.
General Results.
1. The branches of the bridge y with the exception of the one
lying opposite the line, must be equal to each other, and severally
equal to half the measured conductor resistance of the line.
2. The branch lying opposite the line should be equal to the
sixth part of the measured conductor resistance of the line; and
only in this, the smallest of all the branches, should readjustment of
balance be made.
Nos. 1 and 2 necessitate the alteration of all the branches if
\i, the measured conductor resistance, alters within wide limits.
A determination of L will therefore be required from time to time.
Digitized by VjOOQ IC
188 On the Coloured Wnge of Uniaccial and Biaxial Crystals.
From the development of these general retulti it frill be evi*
dent that they fulfil the following conditions :— i»
I. 7%6 irregtdarity of signals in the one station is entirely inde^
pendent of the irregularity of signals in the other station,
U. The irregul^irity of signals in each statitm is due only to
balance not being rigidly established.
III. If balance in either station is disturbed, a single adjustment
in the branch b will reestablish that balance.
IV. Any disturbance of balance will have the least possibh
effect on the received signals.
V. Maximum current at balance.
VI. Maximum magnetic effect of the maximum current on the
receiving'instrument.
[To he continued.]
XXI. On a simple Arratwement by which the Coloured Rings of
Uniaxial and Biaxial Crystals may be shown in a common Mi*
croscope. By Dr. W. H. Stonb*.
THE author was not aware that any arrangement had been
hitherto supplied to the ordinary microscope other than an
extra top to the eyepiece containing a supplementary stage and
an analyzer. This could only be considered a clumsy expedient.
The objects to be obtaineci were clearly two : — ^first, to transmit
the ravs at considerable obliquity through the' plate of crystal ;
secondlvj to gather these up and form a real image within the
tube of the microscope. Amici had accomplished this by a
special combination of lenses which bears his name ; it might,
however, be done simply by placing a screwed diaphragm
on the end of the upper araw-tuoe within the body of the mi-
croscope. The screw should be that ordinarily used for object-
glasses. To this an object-glass of long focus was fitted, and
another of higher magnifying-power in the usual place. The
whole body was then drawn out and adjusted to a telescopic
focus on a distant object. The lower objective formed the
object-glass of the telescope, and the inner objective with the
Huygenian eyepiece a compound ocular. On reinserting the
body thus arranged, and illuminating the crystal on the stage
with convergent light by means of a condenser, the rings and
brushes could be perfectly seen. The whole double series of
rings in a biaxial crystal of carbonate of lead was thus shown.
The condenser used was a '' kettle-drum " of two plano-convex
lenses. The objective on the nozzle of the microscope was a f
of Ross; that within the draw-tube a 3-inch objective of the
same maker.
* Read before the Ph^-«ici4 Spn^t^i June 13, 1874. Comoniiucated by
the Society.
Digitized by VjOOQ IC
[ 189 ]
XXII. Modijhation of the utual Trombone Apparaiuif^
the Interference of 8o9mi4>earmg Wavet. By W. r. BabbbtTj
F.I18.E. hie., Profeeeor of Phyeia in the Royal College of
Science, Dublin*.
A SIMPLE apparatus for showing the interference of sound,
bearing waves may be made by employing a circular
arrangement of tubes, one sliding within the other. One tube,
A, to which the mouthpiece M is fixed, is three fourths of •
circle ; the other tube, B, to which the n<»ile N is attached, is
half a circle, and of such diameter that it slides freely over the
tube A.
When the nossle is diame-
trically opposite the mouth-
piece, the path of the sound-
waves is of equal length, and
hence the sound from any
convenient source placed near
to or within the mouthpiece
is distinctly heard. By tum-
ingthenozzletowardsN^nthe
direction shown by the dotted
lines, one limb of the tube
is lengthened whilst the other
is correspondingly shortened;
the path of the waves being
now unequal, a point is soon
reached where tne sound is nearly obliterated.
Employing a suitable source of sound, and a sensitive flame
or a resonant jar as a phonoscope, an audience can perceive at
once the gradual destruction of the sonorous pulses ; and more-
over the relative lengths of the two branches of the tube clearly
indicate the principle of interference thus illustrated.
One instrument I made was 2 feet in diameter, of 1-inch-
square zinc tubing; another and better instrument (skilfully
made by Mr. B. H. Bidout) was of brass tubing, 1 foot in
diameter, the one limb being ^inch, the other |^inch tube.
About 18 inches in diameter would probably be the best and
most convenient size. In making the experiment, care should be
taken to avoid {a) the conduction of sound to the ear by the
metal substance of the instrument; (13) the direct transmis-
sion of sound through the surrounding air. The latter can be
overcome by attaching a sufficiently long gutta-percha tube to M,
* Read before the Physical Society, June 20, 1874. Commuiiicated
by the Sodety.
Digitized by VjOOQ IC
140 Notices rejecting New Books.
thus removing the mouthpiece to a diBtance from the ear. The
former can be obviated to some extent by having an inelastic
mouthpiece or similar covering to the end of the tube. But
Mr. Woodward's device of putting a source of sound, such as a
reed, entirely within the tube, and a trumpet mouthpiece at N,
is undoubtedly the best and most suitable class method of making
the experiment.
. F.S. — ^With an ordinary pitch-pipe inserted at N, I have to-day
(July 26) repeated the experiment to the class of science teachers
now at South Kensington. A continuous blast of air was driven
through the pipe from an acoustic bellows ; and the loud note
heard at first was utterly extinguished by altering the relative
lengths of the tubes. By pushing the tube still further round
the note again came out; thus the sound of the pitch-pipe could
be turned on and off at pleasure. Extinction is not confined to a
mere line in adjusting the pipe, but spreads over a short and
definite range. In this case it is probaoly, as Professor Ooodevc
suggests, the interference of two resonant columns of air, rather
than the coalescence of two progressive waves in opposite phases.
XXIII. Notices respecting New Books.
Statique ExperimentaU et Theorique des Liquides soumis aux seuUs
Forces MoUculaires, Par J, Plateau. 2 vols. 8vo, pp. 450 &
495. Ghent and Leipzig : F. Clemm. London : Trubner & Ca
1873.
T^HIS work consists essentially of the collected series of papers
-■- "On the Figures of Equilibrium of a liquid Mass without
Weight," which the distinguished physicist of Gthent has published
in the * Memoirs of the Bel^n Academy of Sciences ' during the
years 1843 to 1868. The substance of these papers having appeared
Irom time to time in the pages of the * Philosophical Magazme,' in
the form of comparatively full abstracts of the original memoirs, it
is not needful to say much here by way of introducing or recom-
mending the work to our readers. It should be observed, however,
that this book is not merely a republication, offering simply the
convenience of presenting in a collected form results whicn were
previously accessible only in a number of separate papers published
at intervals during a period of twenty-five years ; thanks to the
careful revision which the whole has received, and to numerous ad-
ditions (some of them of considerable extent, relating chiefly to the
work* of other investigators in the same field of research), the work
before us possesses much of the continuity and completeness of a
systematic treatise.
The chief scientific interest of the phenomena which Professor
Plateau has investigated lies in the simplicity of the physical prin-
ciple to which they are all of them referrible, and in the compre-
Digitized by VjOOQ IC
Notices respecting New Books* 141
hensiveness of the geometrical relation which forms the mathematical
expression of this principle. But, independently of these characters,
which are inherent in the nature of the phenomena, and not liable
to modification in consequence of the greater or less power brought
to the study of them, the present book derives a special value and
beauty from the sagacity with which the author has followed out
the physical and mathematical consequences involved in the prin-
ciple of the equality in all directions of the tension of a liquid sur-
face, and in the resulting geometrical relation of the constancy of
the sum of the principal curvatures of such a surface, comlnned
with the completeness and accuracy of the experimental verification
of theoretical deductions which he has obtained. In fact, the judg-
ment and ingenuity shown in devising the methods of experiment,
and the skill with which they have beien applied, have enabled the
author to trace out, with a minuteness that has not often been
equalled in other branches of Physics, the characteristics of the phe-
nomena under investigation. These phenomena also being compa-
ratively simple, in the sense of its being possible to isolate almost
completely by the methods adopted the effects of the particular
causes it was the author s object to study, these researches form a
remarkable example of the close correspondence between theory
and experiment, worthy to be compared with Schwerd's memo-
rable work on the Phenomena of Diffraction, a work with which
Professor Plateau's presents another point of analogy in the familiar,
every-day character of many of the phenomena with which it deals.
ContrihiUioTis to Selenography, By William Eadclifp Bibt,
FJl^AJS,, F.M.S. London : Taylor and Francis. 1 874.
We are glad to see, by a copy of the above work which we have
received for review, that Mr. Birt has put together in one volume
his more recent labours connected with Selenography ; for not only
are there to be found among them able discussions of matters con-
n3cted very closely with interesting questions of present interest in
t*ie science, but we are convinced, from a careful examination of
Mr. Birt's production, that it will prove of great value to every
shident of the lunar surface who may possess a copy — and that
not only because in future years it will be a work to which the ama-
teur may turn to compare his own observations with those there
recorded of some of the most minute of all lunar objects, in the full
confidence that they were carefully drawn and correctly described
for the epochs of observation, but because it is a volume likely to
be of essential service to every real student in connexion with his
own method and mode. Headers of the Eeports of the British As-
sociation for the Advancement of Science will remember that in
1864 the Association voted a grant for the purpose of mapping the
surface of the moon, which was continued for three years — the re-
sult being that three areas of the contemplated map, on a scale of
230 inches to the moon's diameter, by Mr. Birt, with catalogues <rf
the objects, were published in the volumes for 1866 and 1868. The
first of Mr. Birt's contributions to Selenography, published inde-
Digitized by VjOOQ IC
142 Notkes respecting New Booh,
pendentlj of the Assodatioii in 1870, is a fourth area of tiie map*
in continuation of the original jphm, and which occupies the first
pkce in the present Yolume. Facing page 1 we have an excellent
map of the area, carefully drawn in outline, accompanied hy a full
descriptive Catalogue oi 99 craters and other objects situated upon
the area. The description is completed by a comparison of four pno-
tograms* The numerous notes and woodcuts of interesting objects
must be highly suggestive to every earnest stud^it.
The very complete monograph of the Mare Serenitatis is of itself
a work capable of sustaining the reputation of the author of the
four areas, comprising as it does so large a descriptive catalogue of
objects within tnu) la^e and perhaps b^t*known of all lunar plains,
supplemented by copious notes, and illustrated by a map completely
crowded with objects, some of them very small indeed. As f^ as
we are able to judge, it is quite a model production. It also con-
tains a very- interesting examination of Schroter's drawings of the
region, and a comparison of them with recent photograms and ^e
present appearance of the plain.
Uipparchus is the subject of another masterly monograph, illus-
trated by a well-eugraved map, accompanied by a full catalogue of
objects and numerous descriptive notes, together with a comparison
of the region on different photograms. The scale of the map is
100 inches to the moon's diiuneter. We notice that the paging of
the letterpress of Bipparchtu runs on from that of ihe Mare Sere--
nitatis, from which we suppose other monographs are to follow.
Certainly every lunar observer must hope that may be the case ;
indeed the continuance of the areas of the map is a very desirable
thing while we have nothing at all of the kina which depicts one
hundredth of the lunar features revealed by the average telescope
now in the hands of amateurs. Beer and Madler's map was a
worthy work in 1837 ; but nearly forty years have brought about
great improvements in instruments tor the purpose of observa-
tion, and, as it seems to us, a map which would bring sel^io-
Rraphy more nearly level with the times is really an important
desideratum.
Following the three maps to which we have referred, we have
specimens of the Catalogue of Lunar Objects according to ihe plan
originally devised by lkj&. Birt. This catalogue certiunly has the
merit of clearness and conciseness ; and, by means of a most useful
accompanying table of references and synonyms, the student is able
easily to compare the notes of difEerent observers and authors on
each particular locality which may be under discussion. This is a
valuable adjunct to the descriptive notes and illustrations. What
oiur star-catalogues are to stdlar observers, that would Mr. Birt's
projected work be to students of the moon, if it were only carried
out to completion. The method of arrangement adopted through-
out all Mr. Birt's productions seems to be a specialite of his own.
Other works on the moon mo could name, written in what is called
the popular style, and illustrated by excellent pictorial representa-
tions of the general character of the lunar surface ; but from all
Digitized by VjOOQ IC
Royal SoeUiy. 143
tiieae, which Are more suited to the general reader, the Ydame be-
fore us differs in kind ; and those who desire to be reaUy acquainted
wit^ ihs pumUer detail* of the yarious regions treated of will find
that Mr. Birf s work treats of these especaally • Herein it is unique,
and contains a mass of yaluable information to be met with, so far
as we know, in no other work extant. Indeed all Mr. Birt's maps
and notes are distinguished bj a painstaking accuracj that will con-
fer upon them great value shoula another case arise similar to that
of LiiiiU in any of the areas already completed ; for there will be
found every known spot, streak, craterlet, or other feature de-
scribed, and often distinctly illustrated; so that, so far as this
work is concerned, no future selenographer will be likely to be
misled.
Anotiier portion of the volume is occupied by two series of
papers, entiued '* Selections from the Portfolios of the Editor ot
the Lunar Mf^ and Catalogue/' in the preparation of which Mr.
Birt has been assisted by gentlemen who have given scnne attention
to selenography, and in which will be found many very interesting
papers. EspeciaUy noticeable is one by the Bev. T. W. Webb,
•« On the Study of Change in the Lunar Surface," and another by
Messrs. Webb and Birt on the formation named Cleomede$. The
latter contains formula for computing the length of a measured
line on the moon's surface in English feet, in itself a really impox^
tant acquisition to every selenographer. Many other papers, treat-
ing of various topics, mil be found suggestive.
From a notice on the wrapper of the second issue of the '* Selec-
tions," we learn that increased subscriptions are required to con-
tinue them. But we cannot suppose that the want of subscriptions
is dependent upon any inferiority in the work itself, but rather on
its being not generally known amongst astronomers, and also on
the absence of an interest in the study of the moon's surface, which
contrasts so remarkably with the assiduity with which amateurs
prosecute their studies in other branches of astronomy. We there-
fore hope that before long we shall be called upon to notice a f ur^
ther contribution to selenography by Mr. Birt.
XXIV.. Proceedings qf Learned Socieiiei.
ROYAL SOCIETY.
[Continued from p. 720
January 29, 1874. — Joseph Dalton Hooker, O.B., President, in
the Chair.
'^PHE following communication was read: —
-•- " On the Comparative Value of certain Geological Ages (or
groups of formations) considered as items of Geological Time."
Bj A. C. Eamsay, LL.D., V.P.E.S.
The author first renews briefly several methods by which
attempts have been made to estimate the value of minor portions
Digitized by VjOOQ IC
' 144 Royal Society : — ^Prof. A. C. Ramsay on the
of geological time, such as: — calculations intended to estimate
the age of deltas, founded on the annual rate of accumulation
of semments ; the astronomical method foUowed by Mr. Croll, in
connexion with the recurrence of glacial epochs; the relative
thicknesses of different formations; and the relation of strong
unconformity between two sets of formations in connexion with
marked disappearance of old genera and species, and the appear-
ance of newer forms. Having shown that none of these metliods
give any clear help in the absolute measurement of time in years
or cycles of years, even when founded on well-established facts, he
proceeds to attempt to estimate the comparative value of long por-
tions of geological time, all of which are represented by im-
portant series of formations.
The author then alludes to the subject of two papers by himself,
S'ven^ to the Geological Society in 1871, on the Red Rocks of
ngland, in which he attempted to show that the Old Red Sand-
stone, Permian, and New Red series were all deposited in great
inland lakes, fresh or salt ; and this, taken in connexion with the
wide-spreading terrestrial character of much of the Carboniferous
series, showed that a great continental age prevailed over much
of Europe and in some other regions, from the close of the Silu-
rian epoch to the close of the Trias. He then endeavours to show
the value of the time occupied in the deposition of the above-
named formations, when compared \iith the time occupied in the
deposition of the Cambrian and Silurian strata, and of the marine
and freshwater strata which were deposited between the close of
the Triassic epoch and the present day.
After alluding to the probable mixed estuarine and marine cha-
racter of the purple and grey Cambrian rocks of St. David's, it is
shown that the Cambrian and Silurian series may be massed into
three great groups : — first, from the bottom of the purple Cambrian
rocks to the top of the Tremadoc slates ; these being succeeded
iinconformably by the second group, the Llandeilo and Bala or
Garadoc beds ; on which rest unconformably the members of the
third series, ranging from the base of the Upper Llandovery to
the top of the Upper Ludlow beds, — each imconformable break
in stratigraphical succession being accompanied by a correspcnding
break in paiseontological succession.
These three great divisions are next shown to be comparable,
in the time occupied for their deposition, to the three divisions
of Lower, Middle, and Upper Devonian rocks, which are consi-
dered to be the marine representatives of the Old Red Sand-
stone ; and therefore it follo\*'s that t?ie time oc^mpied in the depo-
aition of the latter may have been as long as that taken in the deposition
of the Cambrian and Silurian series. This position is strengthened
by the great palfiBontological differences in the fossils of the Upper
Ludlow and those of the marine Carboniferous series, which seem
to indicate a long lapse of time during which, in Old Red Sandstone
areas, no direct sequence of marine deposits took place.
The next question considered is, what relation in point of time
Digitized by VjOOQ IC
Comparaiive Value of certain Geological Affei. 145
the depositioii of the Old Bed Sandstone may have taken, when
compiled with the time occupied in the deposition of certain
members of the Mesozoic formations. Through a series of argu-
ments, lithological, stratigraphical, and pal»ontoiogical, the oondu*
sion is arrived at, that the whole of the Liassic and Oolitic series
present the various phases of one fades of miurine life, and, in tiiis
respect, are comparable to the changes in the fossil contents of the
various subformations of the Cambrian and Lingula-flag series,
of which the Tremadoc Slates form an upper meml^r. In
like manner the Lias and Oolites may be compared with the
Lower Devonian strata ; and therefore a lower portion of the Old
Red Sandstone may have taken as long for its deposition as the whole
of the time occupied in the deposition of the Jurassic series.
Following out this train of argument through the Neoccnnian
and Cretaceous strata, the result is arrived at tlMt the whole of
the time occupied in the deposition of the Old Red Sandstone may
have been equal to the whole of the time occupied in the deposition
of aUthe Jurassic, WeaMen, and Cretaceous strata collectively.
In the same manner the next term of the Continental era, tha
Carboniferous epoch, is compared with the Eocene period, both
being locally of marine, estuarine, freshwater, and terrestrial
origin, and both connected with special continental epochs. Next
comes the Permian series, comparable in its lacustrine origin to
the Miocene strata of so much of Eur(^, though in the case of
the Permian watery the lakes were salt. After this the Triassic
series of Europe alone remains of the old continent, the maiine
and salt-4ake strata of which are not likely to have taken a shorter
time in their deposition than the older Pliocene strata.
If the foregoing method be of value, we arrive at the general con-
clusion that the great local continental era, which began voith the Old
Red Sandstone ami closed with the New Red Marl, is comparable, in
point of Geological Time, to that occupied in the deposiUon of the whole
of the Mesozoic series later than the New Red Marl, and of all the Cai-
nozoic formations, and, nufre probably, of all tlie tims that has elapsed
since ^ beginning of the deposition of the Lias down to tJie present
day; and consequently the more modem continental era, which
locally began with the Eocene period and lasts to the present day,
has been of much shorter duration.
The author then pointed out that during the older continental
era there flourished two typical floras — one extending from the
time of the Old Bed Sandstone to the close of the Permian strata ;
while the second, which is largely of Jurassic type, characterized
the Triassic formations. From the time of the Lias onward in
time, we have also two distinct typical floras — ^the first of Jurassic,
and the second of much more modern type, beginning with the
Upper Cretaceous strata of Aix-la-Chapelle and lasting to the pre-
sent day.
In like manner the faunas connected with the land resolve them-
selves into two types : — ^the first chiefly Labyrinthodontian, as shown
in the Carboniferous and Permian strata ; and the second charac-
Phil. Mag. S. 4. Vol. 48. No. 316. Aug. 1874. L
Digitized by VjOOQ IC
146 Royal Sociehj : — ^Piof, 0. Eeyiu)lda on Surface-forces
twiBiic of ihe Tzias, vith [Crocodilift, many land-lkards, Aiiomo-
doDtia, Deinosauria, and Marsupial MaHunalia. This buna, as
regards genera, with the exception of Labynnthodontia and the
appearanoe of Fterosauiia, is represented through the remaining
members of the Mesosoic formations, from Jurassic to Creta-
ceous indusive. After this comes the Pachydermatous Mammalian
Eocene fauna, and after ihaJb the Miocene land-fauna, which,
in its main diaracters, is of modem type. From Jurassic to Cre-
taceous times, indusively, there was therefore, as far as we know,
in this area a land-&una chiafly^Be^tilian, iSaurian, and Marsupia],
and in Tertiary times diiefly Beptilian and PlaoenUl. (Illusianted
b^ a Table.)
In conclusion, the recent character c^ the early nuucine faunas
of the Cunbrian and lingula-fleg series was pcMnted out, such
as Spongida, Annelida, Ediinodermata, Crustacea, Polyioa, Bra*
dnopoda, Lsmellibram^iata, Pteropoda, Nudeobranobiata, and Ce-
phalopoda. This was kmg ago insisted on by Professor Huxley ;
and we find no evidence of its having lived near the beginning
ci the zoological series; for below the Cambrian series we fure
at once involved in a sort of duios of metamorphic strata. Of
tbe geological history, in the words oi Darwin, '* we possess the
last volume alone, rdating only to two or three countries.^ The
connexion of this question with that of the comparative value oi
different geological eras is obvious, especially in rdation to the
palieontological part of the question.
June 18. — Joseph Daltim Hooker, C.B., President, in the Chair.
The following communication was read : —
*\0a the Forces caused by Ev^)oration from, and Cond^isation
at, a Surface." By Prof. Osborne Beyndds, of Owais College,
Manchester.
It has been noticed by several philosophers, and particularly by
Mr. Crookes, that, under certain cuxnimstances, hot bodies appear to
repel uid cold ones to attract other bodies. It is my object m this
paper to pdnt out, and to describe experiments to prove, that
liiese effects are the results of evaporation and condensation, and
that they are valuable evidence of the truth of the kinetic theory
of gas, viz. that gas consists of separate molecules moving at great
velocities.
The experiments of whidi the explanation will be given vrere as
f dlows : —
A light stem of glass, with pith-balls on its ends, was suspended
by a silk thread in a glass flask, so that the balls were nearly at
the same level. Some water was then put in the flask and boiled
until all the air was driven out of the flask, which was then corked
and allowed to cod. When cold there was a partial vacuum in
it, the gauge showing from | to | of an inch pressure.
It was now found that when the flame of a lamp was brought
near to the flask, the pith-ball which was nearest the flame was
driven away, and ihat with a piece of ice the pith was i^tracted«
Digitized by VjOOQ IC
caused by Evaporation and Con4en$aiion. 147
This expenment wm rroeated under a rmety of drcomstances,
in dilEeient Badk» and with different balaxioes, the stem bmngiome-
times of glass and sometimes of platamun ; the results, howeyer,
were the same in all cases, except such variations as I am about to
describe.
The pith-balls were more sensitive to the heat and oM when the
flask was cold and the tension within it low ; but the effect was
perceptible until the gauge showed about an inch, and even after
that the ice would attract the ball.
The reason why ^e repulsion from heat was not apparent at
greater tensions, was deaiiy due to ihe convection-currentB which
the heat generated within the flask. When there was ^lough
vapour, these currents carried the pith witli them ; they were, in
&ct, then sufficient to overcome the forces which otiierwise moved
the pith. This was shown by the fact that when the bar was
not quite level, so that one ball was higher than the other, th6
curr^its affected them in different degrees ; also that a different
eSeet could be produced by raising or lowering the position of the
flame.
The condition of the pith also perceptibly affected the sensitive-
ness of the balls. When a piece of ice was placed against the side
of the glass, the nearest of the pith-balls would be £awn towards
the ice, and would eventually stop opposite to it. If allowed to
remain in this condition for some time, the vapour would con-
dense on the ball near the ice, while the other \M would become
dry (this would be seen to be the case, and was also shown by the
tipping of the balance, that ball against the ice gradually getting
lower). It was then found, when the ice was removed, that the
dry ball was insensible to the heat, or nearly so, while that ball
which had been opposite to the ice was more than ordbarily sen-
sitive.
I£ the flask were dry and the tension of the vapour reduced
with the pump until the gauge showed | of an inch, then, although
purely steiun, the vapour was not in a saturated condition, and
the pith-balls which were dry were no longer sensitive to the lamp,
although they would still approach the ice.
From these last two &cts it appears as though a certain amount
of moisture on the balls were necessary to render them sensitive to
the heat.
In order that these results might be obtained, it was necessary
that the vapour should be free from air. If a small quantity
of air was present, although not enough to appear in t^e gaue^e,
^e ^ects rapidly diminish^, partictdarly that dE the ice, until nie
C(mvecti(m-currents had it all their own way. This agrees with the
&ct that the presence of a small quantity of air in steam greatly
retards condensation and even evaporation.
With a dry flask and an air-vacuum, neither the lamp nor the
ice produced their effects ; the eonvection-currrats reigned supreme
^n v(^hen the gauge was as low as | inch. Under these circum-
sUno^s the lamp generally attracted the balls and the ice repelled
L2
Digitized by VjOOQ IC
148 Roifal Society :-*VroL 0. Reynolds on Sw/ace-forces
them ; i. e» the curreoits carried them towards the lamp and from
the ice ; but, by placing the lamp or ice very low, the reverse effects
could be obtained, wfajjch goes to prove that they were the effects
of the currents of air.
These experiments appear to show that evaporation from a sur-
face is attended with a force tending to drive the surface back, and
condensation with a force tending to draw the surface forward.
These effects admit of explanation, although not quite as simply
as may at first sight appear.
It seems easy to omc^ve that when vapour is driven off from a
body there must be a certain reaction or recoil on the part of the
body ; Hero's engine acts on this principle. If a sheet of damp
paper be held before the fire, from that side which is opposite to
the fire a stream of vapour wHl be drawn off towards the fire wil^
a perceptible velocity ; and therefore we can readily conceive that
there must be a correspcmding reaction, and that the paper will be
forced back with a force equal to that which urges the vapour f or^
wards. And, in a similar way, whenever condensation goes on at
a surface it must diminish the pressure at the surface, and thus
draw the surface forwards.
It is not, however, wholly, or even chiefly, such visible motions as
these that afford an explanation of the phenomena just described.
If the only forces were those which result from the perceptible
motion, they would be insensible, except when the heat on the
sur&use was sufficiently intense to drive the vapour off with con-
siderable velocity. This, indeed, might be the case if vapour had
no particles and was, what it appears to be, a homogeneous elastic
medium, and if, in changing from liquid into gas, the expansion
took place gradually, so that the only velocity acquired by the vapour
was that necessary to aUow its replacing that which it forces
before it and giving place to that which follows.
But, although it appears to have escaped notice so far, it follows,
as a direct consequence of the kinetic tbeory of gases, that, when-
ever evaporation takes place from the surface of a solid body or a
liquid, it must be attended with a reactionary force equivalent to
an increase of pressure on the surface, which force is quite in-
dependent of the perceptible motion of the vapour. Also, conden-
sation must be attended with a force equivalent to a diminution of
the gaseous pressure over the condensing surface, and likewise
independent of the visible motion of the vapour. This may be
shown to be the case as follows : —
According to the kinetic theory, the molecules which constitute
the gas are in rapid motion, and the pressure which the gas exerts
against the bounding surfaces is due to the successive impulses of
these molecules, whose course directs them against the surface, from
which they rebound with unimpaired velocity. According to this
theory, therefore, whenever a molecule of liquid leaves the sur&ce
henceforth to become a molecule of gas, it must leave it with a
velocity equal to that with which the other particles of gas re-
bound ; that is to. say, instead of bebg just detached and quietly
Digitized by VjOOQ IC
earned by Evaporation and Condeniation. 140
passing off into the gas, it must be shot off with a Telocity greater
than that of a cannon-ball. Whateyer may be the nature of the
forces which give it the velocity, and which consume the latent
heat in doing so, it is certain, from the principle of conservation
of momentum, that they must react on the surface with a force
equal to j^hat exerted on the molecule, just as in a gun the pressure
of the powder on the breech is the same as on the shot.
The impulse on the surface from each molecule which is driven
off by evaporation must therefore be equal to that caused by the
rebound of one of the reflected molecules, supposing all the mo-
lecules to be of the same size ; that is to say, since the force of
rebound will be equal to that of stopping, the impulse from a par-
ticle driven off by evaporation will be half the impulse received
from the stopping and reflection of a particle of the gas. Thus
the effect of evaporation will be to increase the number of impulses
on the surface ; and although each of the new impulses will only be
half as effective as the ordinary ones, they will add to the pressure.
In the same way, whenever a molecide of gas comes up to a
Bur&ice and, instead of rebounding, is caught and retained by the
surface, and is thus condensed into a molecule of liquid, the impulse
which it will thus impart to the sur&ce will only be (me half as
great as if it had rebounded. Hence condensation will reduce the
magnitude of some of the impulses, and therefore will reduce the
pressure on the condensing surface.
For instance, if there were two surfaces in the same vapour,
one of which was dry and the other evaporating, then the pres-
sure would be greater on the moist surface than on that which
was dry. And, again, if one of the surfaces were dry and the
other condensing, then the pressure would be greater on the dry
surface than on that which was condensing. Hence, if the opposite
sides of a pith-ball in vapour were in such different conditions, the
ball would be forced towards the colder side.
These effects may be expressed more definitely as f oUows : —
Let V be the velocity with which the molecides of the vapour
move,
p the pressure on a unit of sur&u^,
d the weight of a unit of volume of the vapour,
w the weight of liquid evaporated or condensed in a second ;
then the weight of vapour which actually strikes the unit of dry
surface in a second will be
dv
and the pressure p will be given by
and/ (the force arising frcnn evaporation) will be given by
- wv
* See Maxwell, 'Theory of Heat»' p. 294.
Digitized by VjOOQ IC
ISO Royal Sodtty ;— Prof. O. Reynoldi on Sttrfaet-forca
thorefore
Thus we hare an expresBioii for the force in terms of the qnaiH
titj of watw evaporated and the ratio of the pressure to^the imf
Bit J of the yapour; and if the heat neoessary to evaporate the
liquid (thd ktent heat) is known, we can find the force which
would result from a given expenditure of heat.
Applying these results to steam, we find that, at a tmnperatore
of 60 , the evaporation of 1 lb. of water from a surfaoe would be
sufficient to maintain a force of 65 lbs. for one second.
It is also important to notice that this force will be proportioaial
to the square root of the absolute temperature, and, oonseqnenily,
will be approximately constant between temperatures of 32° and
212°.
If we take mercury instead of water, we find that the force is
only 6 lbs. instead of 65 lbs. ; but the latent heat of mercury is only
^ that of water, so that the same expenditure of heat would main-
Uin nearly thi-ee times as great a force.
It seems, therefore, that in this way we can g^ve a satisfactory
explanation of the experiments previously described. When tiiie
radiated heat from the lamp falls on the pith, its temperature will
rise, and any moisture on it ^vill begin to evaporate and to drive
the pith fro«n the lamp. The evaporation will be greatest on that
ball which is nearest to the lamp ; therefore this ball will be driven
away until the force on the other becomes equal, aftei^ which tiia
balls will come to rest, unless momentum carries them further.
On the other hand, when a piece of ice is brought near, the tem^
perature of the pith will be reduced, and it will condense the va*
pour and be drawn towards the ice.
It seems to me that the same explanation may be given of Mr.
Crookes's experiments ; for, although my experiments were made on
water and at comparatively high pressures, they were in realify
undertaken to vemy the explanation as I have given it. I used
water in the hope oi finding (as I have found) that, in a conden-
sable vapour, tne results could be obtained with a greater density
of vapour (that is to say, with a much less perfect vacuum), the
elEect being a consequence of the saturated condition of the vapour
rather than of the perfection of the vacuum.
Mr. Oookes only obtained his results when his vacuum was
nearly as perfect as the Sprengel pump would make it. Up to this
point he had nothing but the inverse effects, viz. attraction with
neat and repulsion with cold. About the cause of these he seems
to be doubtful; but I venture to think that they may be entirely
explained by the expansion of the surrounding gas or vapour, and
the consequent oonveotion-cun^ents. It must be remembered that
whenever the air about a ball is expanded, and thus rendered
lighter by heat, it will exercise less supporthig or floating power
on the ball, which will therefore tend to sink. This tendency will
Digitized by VjOOQ IC
caused by Evaporution and Condensaiion. ISl
be in opposition to the lifting of the Mcendinc current, and it will
depend on the slwpe and thickness of the hsS whether it will rise
or fall when in an ascending enrrent of heated gas.
The reascn why Mr. Crookes did not obtain the same results
with a less iperte(A> Taoanm was because he had then too large a
proportion of air, or non-condensing gas, mixed with the Tapour,
whM^h i^so was not in a state of satimition. In bis experiments
the condensable raponr was that of mercurj, or something whidi
required a siill higher temperature, and it was necessary thi^ the
Tacnam should he ybtj perfect for such Tapour tp be any thing
like pure and in a satmrated condition. As soon, howerer, as this
state of perfection was reached, then the effects were more appa*
rent than in the corresponding ease of water. This agrees well
with the explanation ; for, as preriously shown, the effect oi mercury
would, for the same quantity of heat, be three times as great as
that of water ; and, besides this, the perfect state of the vacuum
would oUow the pith (or whateyer the ball might be) to move much
more freely than when in the vapour of water at a considerable
tension.
Of course this reasoning is not confined to mercuiy and water ;
any gas which is conden»Bd or absorbed by the balls when cold
in greater quantities than when worm would give the same re-
sults ; and, as this property appears to belong to all gases, it is
only a question of bringing the vacumn to the right degree of
tension.
There was one fact connected with Mr. Crookes's experiments
which, independently of the previous considerations, led me to the
conclusion that the result was due to the heating of the pith, and
was not a direct result of the radiated heat.
In one of the experiments exhibited at the Soir^ of the Boyal
Society, a candle was placed close to a flask containing a bar of
pith suspended from the middle : at first, the only thing to notice
was that the pith vras oscillating considerably under the action of
the candle ; each end of the bar alternately approached and receded,
showing that the candle exercised aninfiuenoe similar to that which
might have been exercised by the torsion of the thread had this been
stiff. After a few minutes' observation, however, it became evi-
dent that the oscillations, instead of gradually diminishing, as one
naturally expected them to do, continued ; and, more than this, they
actually increased, until one end of the bar passed the light, after
which it seemed quieter for a little, though the osciUaticms again
increased until it again passed the light. As a great many people
and lights were moving about, it seemed possible that this might
be due to external disturbance, and so its full importance did
not strike me. Afterwards, howe\ er, I saw that it was only to bo
explained on the ground of the force being connected with the
temperature of the pith. During part of its swing one end of the
pith must be increasing in temperature, and during the other part
it must be cooling. JiJid it is easily seen that the ends will not be
hottest when nearest the light^ (xr coldest when furthest away ; they
Digitized by VjOOQ IC
152. Royal Society.
will acquire heat for some time after they have begun to reeede, and
lose it aft^r they have begun to approach. There will, in fact, be
a certain lagging in the effect of the heat on the pith, like that
which is apparent in the action of the sun on a comet, which causes
the comet to be grandest after it has passed its perihelion. From
this cause it is easy to see that the mean temperature of the ends
will be greater during the time they are retiring than while i^-
preaching, and hence the driving force on that end which is leaving
will, on the whole, more than balance the retarding force on that
which is approaching ; and the result will be an acceleration, so that
the bar will swing further each time until it passes the candle, after
which the hot side of the bar will be opposite to the light, and will
for a time tend to counteract its effect, so that the bar will for a.
lame be quieter. This fact is independent evidence as to the nature
of the force ; and although it does not show it to be evi^ration,
it shows that it is a force depending on the t^operature of the pith,
and t^at it is not a direct result of radiation from the candle.
Since writing the above paper, it has occurred to me that, accord-
ing to the kinetic theory, a somewhat similar effect to that of eva-
poration must result whenever heat is communicated from a hot
surface to gas.
The particles which impinge on the surface will rebound with a
greater velocity than that with which Ithey approached ; and con-
sequently the effect of the blow must be greater than it would have
been had the surface been of the same temperature as the gas.
And, in the same way, whenever heat is communicated from a
gas to a surface, the force on the surface will be less than it other-
wise would be, for the particles will reboimd with a less velocity
than that at which they approach.
Mathematically the result may be expressed as follows — the
symbols having the same meaning as before, e representing the
energy communicated in the form of heat, and Sv the alteration
which the velocity of the molecule undergoes on impact. As before,
p=_ort;=V -d'
Therefore, in the case of steam at a temperature of 60^,
•^ 2000
and in the case of air
/as— L.
•'''1400"
and
Digitized by VjOOQ IC
Geological Society. l53
It must be remembered that c depends on the rate at which
cold particles will come up to the hot surface, which is very slow
when it d^nds only on the diffusion of the particles of the gas
infer se and the diffusion of the heat amongst them.
It will be much increased by convection-currents; but these
wiU (as has been already explained), to a certain extent, produce
an opposite effect. It would also seem that this action cannot have
had much to do with Mr. Crookes's experiments, as one can hardly
conceive that much heat could be communicated to the gas or va-
pour in such a perfect vacuum as that he obtained, unless, indeed,
the rate of diffusion varies inversely as the density of a gas*. It
wiD be interesting, however, to see what light experiments will
throw on the question.
GEOLOGICAL SOCIETT.
[Continued from p. 76.]
November 5, 1873.— Prof. Eamsay, F.R.8., Vice-President,
in the Chair.
The following communications were read : —
1. "On the Skull of a Species of IlalitTierium from the lied Crag
of Suffolk." By Prof. W. H. Flower, F.R.S., F.G.S.
The specimen described, which is in the collection of the Rev. H.
Canham, ofWaldringfield, is from the so-called coprolito- or bone-bed
at the bnse of the Red Crag, and presents the usual aspect of the
mammalian remains from that bod. It is of especial interest as
furnisliina: Iho first recorded cvideuce of llie existence in Britain of
animals belonging to the order Sircnia. The fmgracnt consists of
the facial part of the cranium, separated, probably before fossiliza-
tioc, from the posterior part at the fron to-parietal suture, and in a
line descending vertically therefrom. It was afterwards subjected
to severe attrition, by which many of the projecting parts have been
removed ; but sufficient remains to enable its general relationship to
known forms to be determined. The whole of that portion of the
maxillsc in which the molar teeth were implanted is preserved.
The author compared the fossil skull with those of the existing and
extinct spedes of the order, and stated that, while it presents many
characters common to the Manati and the Dugong, there are others
by which it differs from both, the most striking being the more
normal development of the nasal bones and the outer wall of the
nasal fossie, and especially the dentition, in all of which it shows a
more generalized condition. The existence in it of maxillary teeth
removes it still further from Bhytina, In general character the
* June 10. — ProfesKor Maxwell has shown that the diffusion both of heat
and of the gas varies inversely as the density; therefore, excepting for con-
vection-currents, the amount of heat communicated from a surface to a gas
would be independent of the density of the gas, and hence the force /would be
independent of the density; that is to say, this force woidd remain constant
as the vacuum improyed, while the convection-currents and counteracting
forces would gradually diminish. It seems probable, therefore, that Mr.
Crookes's results are, at least in part, due to this force.
Digitized by VjOOQ IC
164 0$ohgkal SoeUiy ;—
molars eorrespond with those of the genus HdUAsrkam^ in which
the anthor oonsiclered that this fossil found its nearest ally in if.
Schitm, Kaup, from the Miooene of the Bhine YaUeyi a fbnnaticm
inwhidi several of the animals of the Bed-Crag bone*hed are known
to oocur. The difPerenoes, however, espeoiallj the larger sue of the
eranium, in the Crag specimen^ and the larger size of its teetb>
induce the author to regard it as a diitinot species, which he pro-
poses to name HalUhsrium Canhamu
2, " New Facts hearing on the Inquiry concerning Forms inter-
mediate between Birds and Beptiles." By Henry Woodward, Esq.,
P.B.S., F.as.
The author, after giving a brief sketch of the Sauropsida, and
referring especially to those points in which the Pterosaurians
approach and differ from birds, spoke of the fossil birds and land
reptiles which he considered to link together more closely the
Sauropsida as a dass.
The most remarkable reoent discoreries of fossil birds are :-*
I. ArchceopUryx macrura (Owen), a Kesozoic type, which has a
peculiar reptilian-like tail, composed of twenty free and apparently
unanohylosed cylindrical vertebr«D, each supporting a pair of quill-
feathers, the last fifteen vertebne having no transverse processes,
and tapering gradually to the end.
II. Ichthyomis dispar (Marsh), discovered by Prof, 0. C. Marsh
in 1872 in the Upper Cretaceous beds of Kansas, XT. S. It possessed
well-developed teeth in both jaws. The teeth are set in distinct
sockets, and are all more or less inclined backwards.
m. Odontopteryx iolmpica (Owen), an Eocene bird from the
London Clay of Sheppev, the skull of which alone has been dis-
covered, has very prominent denticulations of the alveolar margins
of the jaws.
The author then referred to the Dinosauria, some of whidi he
considered to present points of structure tending towards the so-
called wingless birds.
I. CompiOQWiikM hiigipes (A. Wagner), from the Oolite of Solon-
hofen, is about two feet in length, having a small head with toothed
jaws, suDDorted on a long and slender neck.
The iliac bones are prolonged in front of and behind the aceta-
bulum ; the pubes are long and slender. The bones of the fore
limbs are small, and were probably furnished with two clawed
digits. The hind limb is very large, and disposed as in birds, tlie
femur being shorter than the tibia. The proximal division of the
tarsus is anchylosed with the tibia as in birds.
II. The huge carnivorous Megcdosaurus, ranging from the Lias to
the Wealden, had strong but not masslTe hind limbs, and short
reduced fore Hmbs ; it moved with free steps, chiefly if not solely
on its hind Umbs, which is trua also rf the vegetable-eating lisarcb
of the Mesoaoio rooks.
The author next drew attOBtiott to the Frilled Lizard oi Australia,
Cfhlamydifsaurus Kingxi (Gray), which has its fore Hmbs very much
smaller than the hind limbs, and has been observed not only to sit
Digitized by VjOOQ IC
Mr. J. W. Haike on a very large Saurian Limb-bane. 156
up oceasionaQy, Imt to nm habitoally upon tiie gvovmA <m its bind
1^;b, its fore paws not touching the earth, which upright eaiiiage
neceesitatM qMcial mo^ftcations of ibe sacrum and palTio bones.
The Solenhofen limestone, in which Pterosauiia are frequent,
and which baa yielded the remains of ArehcBopUryx and of Cem-'
]^$ognaihus^ has also furnished a slab bearing a bipedal track, re-
sembling what might be produced by Chlamydosauru$ or Comp$o^
ffnathue. It shows a median track formed by the tail in being drawn
along the ground ; on each side of this the hind feet with outspread
toes leave their mark, while the fore feet just touch the ground,
leaving dot-like impressions nearer the median line. Hence the
author thought that, while some of the bipedal tracks which are met
with from the Trias upwards may be the " spoor " of struthious
birds, most of them are due to the bipedal progression of the
Secondary Beptiles.
3. <*Nota on the Astragalus otigwtnodon MawtdU."^ By JT. W.
Holke, Esq., P.B.fl., F.G.S.
The author exhibited and described an astragalus of Iguanod&n
from the collection of E. P. Wilkins, Esq., F.6J9. The bone was
bdieved to be previously unknown. It is a bone of iregular form,
having on its lower surface the characteristio pulley-shape of a
movable hinge-joint The upper surface presents a form exactly
adapted to that of the distal end of the tibia ; so that the applied
surfaces of the astragalus and tibia must have interlocked in such a
manner as to have precluded all motion between them. The author
remarked upon the interest attaching to this fact in connexion with
the question of the relationship between the Dinosauria and Birds.
4. " Note on a very large Saurian limb-bone, adapted fbr progres-
sion upon land, from the Kimmeridge Clay of Weymouth, Dorset.*'
By J. W. Hulke, Esq., F.R.S., F.G.S.
The bone described by the author presents a closet resemblance
to the Crocodilian type of humerus than to any other bone ; and he
regarded it as the left humerus of the animal to which it belonged.
Its present length is 64 inches'; but when perfect it eould hardly
have been less than 68 inches in length. The middle of the shaft
is cylindroid. Its transverse section is of a subtrigonal figure, and
presents a large coarsely cancellated core, enclosM in a compact
cortical ring. The bone is considerably expanded towards the two
extremities ; the distal articular surf&ce is oblong, and divided into
a pair of condyles by a very 'shallow vertical groove; below, the
anterior border, in its proximal half, is much wider than the cor-
responding portion of the posterior border, and is flattened and pro-
duced downwards into a ventrally projecting crest ; and tiio distal half
of this border forms a thin, rough crest, projecting forwards. The
presence of these crests distinguishes the present humerus fh>m
those of Pelorosaufus and of Ceteoeaurus &a<mien$i8 ; but the general
correspondence of th6 bone with the humerus of the latter species
leads the author to refer it provisionally to a species of Ceteommrue,
whicb he proposes to name C hwm^o-irietafus^
Digitized by VjOOQ IC
[ 156 ]
XXV. Intelligence and Miscellaneous Articles.
ON A SIMPLE OCULAR-8FEGTR08COPB FOR 8TAB8.
BT F. SOLLNEli.
^rilE annexed figure shows, of the natural size, the section of a
A compendious form of staivspectroscope in combination with
the ocular of a telescope.
It consists of a small direct-vision prism fixed in a tube CD, the
dispersion of which is about
equivalent to that of the sys-
tem of prisms of a Browning
miniature spectroscope. The
tube C D is movable in a se-
cond tube, A B, which can be
screwed upon the head of the
eyepiece and contains a cylin-
drical lens L of about 100
millims. focal distance. As
the length of the line of light
produced by this lens depends both on its focal distance and also
on the dimensions and proportions of the optical parts of the tele-
scope, it is advisable to have in readiness several cylindrical lenses
of different lengths of focus, so as to be able to employ them ac-
cording to the length of the line of light (and consequently the
breadth of the spectrum) desired.
0^ and O^ are the two lenses of the eyepiece, and hence do not
belong to the spectroscope.
If with this instrument the spectrum of a star is to be observed,
the tube C D vdth the prism is first removed, and the ocular bo ar-
ranged that when the eve is at O a sharp line of light is seen. It
is essential, in doins this, that the eye should be at about the same
distance from the lens L as when the prism is employed. The
tube C D is now inserted, in such a manner that the refracting
edge of the prism lies, as usual, parallel to the luminous line, and
consequently the spectrum attains its greatest breadth. Self-evi-
dently, for a given telescope, the suitable arrangement need only
be once ascertained ; so that then by a small screw S the prism can
be fixed in an invai;^ble position >\ith respect to the cylindrical
lens L. The prism is manufactured by M. Mens, of Munich ; and
he prefers to use it in this compendious form for microscopes.
The intensity of the light of this ocular-spectroscope is so consi-
derable, that, in combination with a small portable telescope, the
objective of which has only 35 millimetres aperture and about 400
millims. focal distance, it shows distinctly the lines of stars of the
first magnitude, such as Wega, a Ononis, and even a Herculis wJieti
the state of tJie atinosphere corresponds^ as Professor Winnecke and
Dr. Yogel convinced themselves and others on the occasion of their
visit to Leipsdg in the course of the past year. When Venus ap-
pears as a slender crescent, its spectrum is singularly beautiful.
Although, according to the well-known methods employed by
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Intelligence and Miscellaneous Articles. 157
Browuiug, Yogel, and others, a scale could be very easily connected
with this instrument, it can be recommended even without one for
systematic mass-observations o£ fixed-star spectra, in which the
prime object is to ascertain the typical constitution o£ the spectra.
As the essential differences between these types probably depends
only on the temperature and mass of those incandescent bodies, and
according to the observations of Secchi and others those types stand
in a certain relation to the distribution of the stars in space, such
systematically conducted mass-observations may in future become
of high importance for the progress of astrophysics.
I permit myself, in conclusion, the remark that the combination
above described was explained and exhibited by me at the last meet-
ing of the Astronomical Society at Hamburg, in September 1873. —
Berichte der Icon, sdchs. Oesellschctft der Wissenschaften math.-phys.
Classe, April 23, 1874.
NOTE ON THE CAUSE OF TIDES* BY £. J. CHAPMAN^ PH.D., PRO-
FESSOR OF MINBBALOOY AND OEOLOOT IN UNIVERSITY CO L«
LEGE^ TORONTO*.
The phenomenon of the tides, stated broadly, consists of a pass-
ing elevation, real or apparent, of oceanic waters at two opposite
points on the surface of the globe. These elevations, which follow
the moon in its course, may become greatly intensified under local
conditions, as where opposing coast-lines impede the progress of
the tidal wave ; but in the open ocean, it is well known, they are
of but slight significance. According to the received theory, they
are occasioned essentially by the unequal degree of attraction ex-
erted by the moon on different parts of the earth — this attraction
being, of course, modified by that of the sun. It is thus assumed
that the waters, owing to their comparative mobility, are drawn
towards the moon on one side of the globe, whilst the solid earth
is drawn away from the waters on the other side — or, to use the
common phraseology, is drawn towards the moon faster than the
waters can follow.
This view, although not without opponents, has been almost uni-
versally adopted in default of a more satisfactory explanation.
The explBoiation of the cause of tides now suggested has at least
this merit : it applies the same principle in elucidation of both tides
— that nearest the moon, and that on the opposite side of the globe.
It is briefly this : — When two bodies pull against each other, there
must necessarily be a contraction of particles towards the centre of
each body along the line of pull or resistance. In the pull, there-
fore, of the earth upon the moon, the earth (and of course the moon
also) must suffer a passing contraction, the part along the line of
pull, so to say, contracting more than the other parts. But this
contraction is mechanical only, and is therefore a compression ; and
* Commiinicated by the Author. Condensed from a commuDioation
made to the Canadian Institute, February 7, IS74,
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158 fnietligence and Miscellaneoui Articles*
M water is practically incompressible, tiie sea remains essentially
unoffectod, whilst the earth shrinks beneath it, and l^us causes the
tide. The shrinkage of course becomes greater, and the tide higher,
when both sun and moon take part in the counter-pull, whether
acting on the same side of the eaiih or on opposite sides. It may
be assumed, however, from the known heignt of the tidal wave
where the march of this wave is unopposed, that the maximum
amount of contraction does not exceed a foot for each thousand
miles of the earth's radius — being thus, in round numbers, less than
one part in five millions. In the tremendous pull of the earth upon
the moon, by which the moon is kept upon its course, a passing
contraction of this comparatively slight amount may be easfly con-
ceived to follow. According to the commonlv adopted theory, one
tide is assumed to result from the withdrawal of the earth, locally,
from the waters above it ; in the view now proposed, both tides are
assumed (although on a different principle) to be thus caused.
ON THE TEMPERATURE OP THE SUN. BY J. VIOLLl.
Several months since, I undertook some experiments to deter-
mine, by various methods, the temperature of the sun. I beg the
Academy to kindly permit me to submit to it the first results St my
researches.
Measurements of solar heat can be made in two ways. In the
first, a thermometer is placed successively during equal times in the
shade and then in i^e sun, and the course of the instrument is folr
lowed in each case : this is the dynamic methody that of the pyrohe-
liometer of Pouillet. In the second the thermometer remains sub-
mitted to solar radiation until the temperature indicated by the
instrument becomes stationary ; and at tne same time the tempe-
rature of the thermometer and that of the enclosure are noted: this
is the static method, that which appears to be adhered to by most
ot the physicists who occupy themselves with the measurement of
solar heat. I shall for the moment speak only of the latter me-
thod, and in the first place copsider its principle.
Let a spherical envelope be maintained at a constant temperature
i, and let the bulb of a thermometer be in i^e centre of the sphere,
which bulb I will for an instant suppose infinitely small. The en-
closure is coated with lampblack, as well as the bulb of the thermo-
meter. Let us suppose equilibrium of temperature established.
The enclosure then sends to the thermometer a quantity of heat Sa<,
a being Dulong's constant or 1*0077 ; and the thermometer sends
back to the enclosure the same quantity of heat Sa^ Let us now
pierce in the spherical enclosure a circular aperture w of such di-
mensions that it will be seen from the centre under the angle which
measures the apparent diameter of the sun, and let us direct this
aperture toward the sun. It is manifest, according to the law of
the variation of calorific intensity inversely as the square of the
distance, that the real action of the sun on the bulb of the thermo-
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Intelligence and Miscellaneoue AriicUi. 160
meter is identical with ihnt which would be exerted by a disk of
8ur&ce M placed at the i^perture (rf our sphere, tius disk haying Uie
same tempeniture and emissive power as iAie sun. We can there-
fore define the temperature of the sun by that whidi would have to
be attributed to this imaginary disk, possessing the emissive power
of lamp]i>Uok, to produce upon the thermometer the same effect
which IS actually produced by the sun. Let a; be t^e temperature^
thus defined, of the sun, 0 the stationary temperature of we ther-
mometer nceinng the solar radiation throu^ the aperture ta ; the
quantity oi heat emitted by the t^rmometer (which was Ba^ at the
temperature t) has become So' ; and putting that quantity ot heat
equal to the sum of the quantities enutted by enclosure and by the
sun, we have at once
This is precisely the equation as written by H. Yicaire ; but it was
established under reserves from which we must now free ourselves.
The dimensions of the thermometer are necessarily finite ; and cof^-
sequently the aperture thrpugh which the solar ravs penetarate must
be widened to permit them to reach the whole of the bulb : hence
comes a double complication.
Let us now consider an admission-aperture Q large enough for
an entire hemisphere of the bulb to receive the rays of the sun. I(
^e diameter of the bulb is sufiiciently small in proportion to that of
the enclosure, every point of it will be sensibly in the same condi-
tions ; so that in order to account for the actual state of the appa-
ratus, it is sufficient to consider any one point whatever ox the
bulb. This point is submitted: — (1) to the radiation of all the
preserved portion of the enclosure ; (2) to the radiation of the sun,
which is equivalent to that of a surface w placed at a distance equal
to the radius of the enclosure and kept at the temperature of the
sun ; (3) to the radiation of the whole of a portion of the sky bor-
dering the sun, which acts as ^ surface Q— im at an unknown tem-
perature y. The precise equation is, therefore,
Sa*« Sa<-f iMa*-f Oay.
I will indicate in a forthcomine note how, making Q to vary by
means of diaphragms pierced with apertures of known dimensions,
the correction-term fl«y can be determined mth sufficient exact-
ness. An idea of its quantity will be given by the following result,
the only one I shall cite at present : —
On March 14, 1874, the sky being very clear, although the ground
was covered with snow, at 1 p.m. the quantity of heat arriving from
the sun at the surface of the ground was the same as that which
would have been given by a disk of the same apparent diameter as
the sun, of maximum emissive power, and at the temperature of
1238*^ C. The temperature of the air was + 1°, and the barometric
pressure 758 millims. In these conditions, the diameter of the
admission-aperture being about 25 times the sun's apparent dia-
meter, the portion of the sky bordering the sun, and seen from the
Digitized by VjOOQ IC
160 Intelligence and Miscellaneous Articles.
bulb of the thermometer, acted as a surface Q heated to near 100^,
the enclosure being at 9^-2. The total intensities of the three
radiations sent to the thermometer by the surfaces S, m, and O were
then sensibly proportional to the numbers 15, 1, and 0*1.
It will not be uninteresting, and I have. already some measure-
ments on this point, to compare at different periods, and especially
at different altitudes, the radiation of this portion of the sky bor-
dering the sun, the illumination of which exhibits at times remark-
able intensity. Perhaps we shall find there a portion of the heat
lost by the direct rays in their passage through our atmosphere. —
Oomptes lUndus de VAcad, des Scietices, May 18, 1874.
ON A PECULIAR PHENOMENON IN THE PATH OF THE ELECTRIC
SPARK. BY PROF. TOEPLER^ OF GRA2.
It is well known that the sparks from the discharge of a Leyden
jar leave upon the surfaces of insulators a trace, conditioned by cer-
tain mechanical processes. The phenomenon is especially charac-
teristic upon very delicately smoked glass surfaces to which sparks
spring between pointed conductors. I have therein observed a re-
gular microscopic structure.
With a length of spark of 4 to 6 centims. the trace is generally
a bright streak 3 mlUims. wide, with a dark axis, produced by the
soot-particles being partly throwTi to the sides, partly going to
the axis and there accumulating. On this trace there is further
found a mostly very striking knot-like thickening just where the
lateral motion of the air has taken place with peculiar violence — a
place in the spark which had already struck me in my optical
observations (Pogg. Ann, vol. cxxxiv.). Before this spot the
trace is altogether different from what it is beyond. Towards
the positive conductor the spark-path is mostly branched off like
a tuft, towards the negative not so. When the trace is ex-
amined with a mcOgnifying-power of 15-20, there appears fre-
quently on the positive side, never on the negative, in the dark
axis of the spark-path a very fine dark zigzag line resembliug a mi-
croscopic sine-curve, of 0- 12-0' 13 millim. wave-length. From the
internal angles of this lino issue laterally equidistant bright streaks
inclined to the axis of the spark in the direction of motion of the
positive electricity. This microscopic structure (the regularity of
which is sometimes surprising) is often found also just as distinct
on the fine side branches which break forth from the positive part
of the spark-path. I remark, further, that the soot-particles wnich
exhibit the structure are in some measure fixed to the glass surface ;
for when the layer of soot is removed, say, with a fine hair pencil,
the dark streak in the axis of the spark remains adhering, though
of course the microscopic delicacy of the figure is destroyed. —
Sitzung der math.-naturiv, Classe dtr haiserl, Akad. d. Wissensch, in
TTtVn, May 15, 1874.
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TH,E
LONDON, EDINBURGH, and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FOURTH SERIES.]
SEPTEMBER 1874.
XXVI. On the Opacity of the Developed Photographic Image,
By Captain Abnby, KE.y F.R.A.8., F.C.S.*
IN a series of pictures of the sun which have lately been taken
by photography^ I found the opacity of the image by no
means varied directly as the time of exposure. This caused me
to institute an inquiry into the relation of time of exposure and
intensity of light on the one hand, and the resulting opacity of
the image on the other.
Primarily it was necessary to obtain some known gradation
of intensity of light, and then to measure the resulting opacities
caused by it on a photographic plate. The gradation was ob-
tained by causing a " star ** to revolve rapidly round its centre.
The " star " was cut out with great exactness from white card-
board and made with eight '' points.^' The curve of each point was
made to take the form of a portion of an equiangular spiral.
By this means an arithmetical progression of white was obtained
when the star was made to rotate. When revolving in front
of a black background, at two inches from the centre of the card
(and within that distance) pure white was obtained ; whilst at
fourteen from the centre pure black was obtained. The black
background employed was of such a dead nature that sunlight
gave no appreciable shadow on it when an opaque body was
placed before it.
The star was made to revolve at the rate of fifty revolutions a
second. In some cases a dead-black star was made to rotate
before a clear sky, the only access of light being through the
openings of the points. •
* Communicated by the Author.
Phil. Mag. S. 4. Vol. 48. No. 317. Sept. 1874. M
Digitized by VjOOQ IC
162
Captain Abney on the Opacity of the
Plated were exposed on this object^ the negatives being ob-
tained by the ordinary wet process, with simply iodised collo*
dion, an 8-per-cent. nitrate-of-silver bath, and 4-per-cent. iron
developer. The strength of the developer was afterwards varied ;
but for the purposes of these experiments any variation was ex-
cluded. Other negatives were obtained on dry {Elates made with
bromised collodion, a 16-per-cent. nitrate-of-silver bath, albu-
men preservative (washed off, after application, as far as possible),
and alkaline development of one particular strength. By alka-
line development, as is well known, the bromide of silver is re-
duced to metallic (or oxide of) silver in situ, no free nitrate of
silver being applied to the image during development. The
opacity of the image obtained by this method is particularly
adapted for giving the necessary means of measuring the action
of any relative intensities of light acting on the silver for any time.
In order to determine the relstive opacities of the image, it
was necessary to obtain some standard scale with which to mea-
sure. The ordinary methods were tried without success, the
image being '' matt,'' or only translucent. Failure with them
was inevitable. After various experiments with coloured gela-
tine wedges, I determined to use coloured glass wedges, and,
owing to the kindness of Mr. Browning, obtained three smoke-
coloured ones, corrected for refraction by crown glass. These
in varying combinations have given me every thing that could be
desired. The mounting I adopted for them is as follows.
Fig.l.
U
A is the wedge in position, B a space in the frame E, in which
any glass whose opacity is to be measured is placed, C a slit,
and D a fixed scale dividing the wedge into arbitrary divisions.
In actual use the whole of the frame was glased with finely
ground glass, the slit being next to it, and the wedge against
that again. When measurements of opacity were taken, the
glass to be tested was nlaced in B and a light placed at a known
distance behind the slit. Great care was taken to ensure the
equal illumination of C. The length of the wedges are severally
6*5 inches. They do not give a sero of absorption at their thin
Digitized by VjOOQ IC
Developed Photogrtqkhic Image. 163
ends^ it being found necessary in grinding to have an appreciable
thickness. I was enabled to calculate the relative absorptive
values of each wedge ; and the following Table will give an idea
of the degree of accuracy with which they were scaled. The
values are given in lengths of a half-inch s(»de, starting from the
calculated sero of the wedge which I have called A. Each of
the wedges were reduced to the same scale. The numbers refer to
different opacities which were measured. A mean of six read-
ings was taken in each case ; and in no instance did any reading
vary more than '15 from the mean.
A.
B.
C.
No. I. .
. 715
718
718
No. II. .
. 10-21
10-20
1018
No. III. .
. 12-44
12-45
12-41
No. IV. .
. 17-60
17-50
17-52
No. V. .
. 18-60
18-52
18-52
From careful measurements it was found that the coefficient
of absorption for each unit of scale of wedge A for the light with
which the measurements were taken was *192.
The photographs of the rotating star were taken of the full
size of the original, only half of the disk being in some cases on
one plate. Strips were cut from these negatives, one edge
always passing through the centre of the image of the star. The
relative transparencies of every \" or ^" were obtained by •com-
parison with the wedges. From these values the accompanying
curves (fig. 2) have been formed, the ordinate being the translu-
cenc^, whilst the abscissa is a measure of the intensity of the
original reflected light. Only four results are shown — ^two ob-
tained by wet, and two by dry plates. About thirty were
measured with almost identical results.
Each strip was compared with the wedge by daylight^ and
also by an artificial monochromatic light. The results obtained
by the one were nearly proportional to those obtained by the
other ; hence only one curve for each strip is given ; and this
was obtained by the latter light. To guard against a false ratio
of intensity of light due to the lens, negatives of the star were
takmi at different parts of the plate, and a mean taken. As the
lens used was non-distorting and of long focus, the edge and
centre of the plate, when directed towards the sky or on a uni-
formly white surface, had sensibly the same illumination. Each
portion of the strip cut from the negative whose opacity was
to be compared was placed above the wedge, at B, and opposite
the slit C. These were clamped together and moved till Ught
from behind, shining through the slit and through the image
and the wedge respectively, appeared of the same brightness on
Digitized by VjOOQ IC
164 On the Opacity of the Developed Photographic Image.
the ground glass. The position of the slit in regard to the scale
was noted, and the intensity of light transmitted calculated by
the ordinary formula. Each strip was compared six times —
three times by myself^ and three times by an assistant. A mean
of the six readings was taken as correct.
Fig. 2.
F C
A and B tre the curves given by the images on the dry plates.
C and D are the curves given by the image on wet plates.
The dotted lines indicate the line whose ordinates give an arithmetic
progression of transparency, £ F being unity or transparency.
FG represents the length of the strips examined, and therefore the
varying intensity of Ught, F being zero and G the maximum.
Regarding the curves given by the dry plates^ if we sup-
pose 'that varying intensities of light cause a corresponding re-
duction of the bromide of silver after development^ it can be
easily demonstrated that the intensity of light passing through
the image after clearing away the unaltered bromide would be
l'=:n.e-", (a)
where n and k are constants depending on the thickness and
opacity of the bromide film^ and I the intensity of the light pro-
ducing any one part of the image — ^that is, on the supposition
that the image is formed of matter continuous but of varying
density. This is not the case^ but there is an approximation to it.
Under the same supposition we can assume that there is a function
of time into a function of intensity of light acting on an infi-
nitely thin layer of the bromide of silver which will cause an
entire reduction of the bromide on development : this we might
call a state of saturation. In the image of the star there may
be some point where the upper layer of bromide (of infinite
thinness) is saturated. From that point along the image to be
produced bv the higher intensities the whole surface is satu-
rated^ and the saturation must gradually approach the bottom
surface. From the point where the whole depth of the layer is
saturated^ along the image to be produced by still higher inten-
Digitized by VjOOQ IC
On the Behaviour of certain Fluorescent Bodies in Castor^oil. 165
sities, there can be no further change. Here it can be demon-
strated that, between the two points above alluded to, the curve
should have the form
V^pl-U-r\ {0)
where p, q,r vre constants, and I is the original variable inten-
sity producing the image. From the last point parallelism
would result, and y would become a constant. Theoretically,
then, the measure of the varying translucency would be com-
pounded of (a), (fi)f and a straight line.
The curves shown above lead us to suspect that this is the
practical result of increase of intensity and time. From other
experiments, however, I am inclined to think that even where
there is no saturation the relation between time and inten-
sity is not so simple as has hitherto been imagined. When
light actually reduces bromide without the aid of a developer,
a compound curve somewhat similar to (a) and 09) will result.
In collodio-chloride printing on glass a like result would oc-
cur. Presumably the same also occurs when printing on albu-
menized paper. The curves deduced by experiment, and also
from calculation, show the reason why iu a negative the detail in
the shadows and highest lights is more difficult to render
faithfully than in the half-tones. They may also show why in
a print the details in the first-named portions is liable to be
obliterated, even should they be well defined in the negative.
The curves measured from the dry plates show that bromide
of silver is less sensitive to low intensities of light than is the
iodide.
The action of different strengths of developers I propose to
treat of in a separate communication, as also the relation between
time of exposure and intensity of light.
XX VII. A Note on the Behaviour of certain Fluorescent Bodies
in Castor-oil. By Charles Horner'^.
SOME colouring-matters derived from woods, not showing
any fluorescence when dissolved in water, alkaline solu-
tions, alum, or alcohol, are found to exhibit this phenomenon on
treatment with castor-oil ; whilst other substances, which fluo-
resce in alcohol &c., are observed to show this property with
augmented intensity.
To obtain clear solutions, the materials are first boiled in
alcohol, filtered, evaporated to dryness, and then heated with
the oil. On transferring some of the prepared solution to a
test-tube and reheating, the fluorescence disappears as the tem-
* Communicated bv the Author.
Digitized by VjOOQ IC
166 Baron N. Schilling on the Constant Currents
Grature approaches the boiling-pointy bat retoms on cooling,
oreover this operation may be repeated without the substances
suffering decomposition. Cudbear, camwood, logwood, and tur-
meric are selected as illustrations of the properties citdl.
Cudbear yields a brilliant orange fluorescent light, and is
idsible in diffused daylight without the agency of a condensing
lens, which is necessary to show it in an alcoholic solution.
Camwood exhibits a powerful apple-green fluorescence,
although wholly destitute of this propeorty in aqueous or alco-
holic media. The spectrum of the fluorescent light is continuous
from E downwards, interrupted by two narrow faint shadings
situated at 8| and 5 of Sorby's soede.
With regard to logwood, unless the castor-oil solution be sa-
turated, sunlight and a lens are requisite to bring out its fluo-
rescent character. The colour very much resembles that of
camwood, but is distinguished by its spectrum, which is conti-
nuous from b, but interrupted by two shadings at 4^ and 5}.
Turmeric is well known to fluoresce powerfully in alcohol a
yellow-green, and in benxole a blue-green. In castor-oil, how-
ever, the fluorescent light is at least three times as bright as
in other fluids, and may be described as a vivid emerald-^reen,
evident in the dullest daylight ; but if a flat bottle of the solution
be placed on black velvet behind rather deep cobalt-glass when
the sun is shining, the phenomenon is of a most brilliant descrip-
tion, and without exaggeration may be compared to that pro-
duced by the beautiful uranium-glass. The spectrum furnished
by the fluorescent light is characterised by transmission of red
and green rays, and blue to F, with a faintly perceptible shading
at the yellow end of the green.
These facts therefore show that, in studying the phenomena
of fluorescence, advantage should be taken, whenever possible,
of this valuable solvent property of castor-oil.
XXVIII. The Constant Currents in the Air and in the Sea : an
Attempt to r^er them to a common Cause, By Baron N. Schil-
ling, Captain in the Imperial Russian Navy.
[Concluded ftrom p. 109.]
AS we are speaking of wave-motion, it will not be out of
place to mention here a circumstance which will subse-
quently be of importance for our argument.
It is that the theory of waves, which is commonly laid as a
foundation for all tidal phenomena, has called forth two views
which cannot possibly be both together correct. In the first
place, it is generally assumed that the flood tide rises just as far
Digitized by VjOOQ IC
in the Air and in the Sea.
167
above the ordinary aea-level aB the ebb sinks below it. Secondly,
it is assumed that the middle time between high and low water
corresponds to the normal level. The highest water is formed
by the two cusps A and E (fig. 8) of the tidal ellipsoid APES,
Fig. 3.
and the lowest bv the circle P S, which halves the surface of the
ellipsoid at its mmor axis. The normal level will therefore, ae-
cording to the common assumption, be found on the circles D C
and i^^ 6, which run parallel with the circle P S and are distant
45^ of arc both from the points A and E and from the circle
PS; so that PF=FE and PC=AC; that is, about three
hours after flood the normal level, and three hours later the ebb
comes in. On this assumption, however, the superficial space
of the surfaces A C D and E F 6 together, occupied by the flood
tide, is 2^ times as small as the superficies of the middle zone
C F O D, in which the water stands at the ordinary level. But
since the water which forms the accumulation of the flood can
only be derived from the ebb-zone, it is clear that, on this assump^
tion, the same mass of water must rise considerably more on the
smaller space than the water-surface sinks in the ebb-zone. If,
on the other hand, we adhere to the assumption that the water
rises as high above the normal level as it sinks below it, the sur^
face occupied by the two floods must be just as great as that
occupied oy the middle ebb-zone, and the two circles at which
the normal level is found must be only 30^ distant from the
central circle, but 60° from the cusps A and E of the ellipsoid.
Flood tide would thus last eight hours, but ebb only four. Or
the water must fall as much in the last two hours of its going
down as in the first four after high water, and likewise rise as
much in the first two hours after its lowest as in the remaining
four. Probably the reality lies between the two assumptions ;
that is^ the rise of the water during flood is probably more con-
siderable than its fall during ebb, and, on the other hand, the
Digitized by VjOOQ IC
168 Baron N. Schilling on the Constant Currents
circles of normal level are more than 45^ and leas than SOP of
arc distant from the cusps of the tidal ellipsoid 'I'.
As at coasts the currents produced by the flow and ebb are
always observed to flow alternately in precisely opposite direc^
tions, it is generally believed that the attraction of the moon and
sun cannot exert any influence on the constant currents. Miihry
says, *' It is scarcely necessary to mention that the tidal motion,
which daily carries its two meridian waves round the globe, is
something altogether different from the rotation-current: the
former extends over all latitudes, and generally occasions no
forward motion of the mass of water, but only waves, t. e. oscil-
lations .... Such an assumption is contradicted also in a pe-
culiarly decided manner by the return* currents flowing on both
sides of the equatorial current in a wide semicircle from west to
east (therefore against the tide-wave) — the compensation-arms
of the rotation-current, which at the same time enclose each a
wide central space filled with still water and floating seaweed,
the Sargasso-seas. How can the tide-wave call forth such phe-
nomena ? We are of opinion, moreover, that, if there were no
moon, the equatorial current would still exist while the earth
revolved on its axis ; but it would not exist if the globe did not
turn on its axis, even though the moon should daily travel round
the earth^t.
We cannot possibly share this opinion of Miihry^s. We will
besides let the thing speak for itself, subjecting the action of the
attraction of the sun and moon to a closer consideration.
Suppose the circle AGED (fig. 4) to be the equator, and
L the centre of the moon, which we will imagine in the plane of
the equator. If, then, the earth had no rotation, the surface of
the sea must take the form of the dotted line aced. To form
this ellipsoid, currents must proceed from all sides towards the
cusps a and e, lasting until the ellipsoid had attained its due
elongation. But since the earth is constantly turning, the moon
relatively to the earth will have already arrived at another point
before the water and the atmosphere have had time to properly
form the ellipsoid aced. Of course the currents will immedi-
diately direct their course to the new point of attraction ; and
since this again alters its position, a current must be produced
in the air and water which must endeavour to follow the motion
of the moon and shift the cusps of the ellipsoid perpetually from
east to west. On the other hand, by the shifting of the moon
* It appears, therefore, that the zero-point of the tide-gauffes has not
et received its true position. This must lead to erroneous resulti in lerel-
Jng-surveys Tvhen the heights of two neighbouring seas are to he compared
in which the heiehts of the tides differ (as, for instance, Panama).
t Miihry, Veber die Lehre von den MeereS'Strommnffen, p. 9.
hi
Digitized by VjOOQ IC
in the Air and m the Sea.
169
from L to I/, all the points in the titeecaf are moved somewhat
nearer to the moon, and therefore the attraction of the moon on
Fig. 4.
A
<fi-
^^^
{-
iT^^
'-^—-^^
\
it^^-^:C^
--"^
\
^=^===
^"^-"^^^--r^
^^,_^
all these points is increased; while every point in the fitc e^da
has removed a little further from the moon, and is consequently
less attracted. We will represent the attraction of the moon by
two threads L c and L d fastened to the circle. We will gradu-
ally more and more draw the thread L c, to represent the con-
stantly augmenting attraction of the point c. We will constantly
let the thread L d give way, to imitate the diminution of the
attraction of the point d. Of course, through greater tension of
the thread Lc and continual yielding of the thread LJ, the
points c and d receive a motion in the direction of the arrows C
and D. This motion will be the quicker the greater the circle
to which the points belong, because in greater circles the change
of distance from the moon, and consequently the alteration of
her attraction, is more considerable for every point than in
smaller circles.
All that we have just said of the moon holds good also for the
sun, with onl^ this difference — that the motions of air and water
produced by its attraction will be somewhat less than those pro-
duced by the moon.
We see therefore that the attractions of the sun and moon
must each present two reciprocally counteracting developments
of force. The one, which cidls forth an east-to-west current and
corresponds to high water, we will henceforth name the flood-
current force ; the other, corresponding to the ebb and impelling
air and water from west to east, we will call the ebb-current
force.
If these two forces are of equal intensity, they will balance
each other and produce no current ; but as soon as one of the
two is greater, the water and air will be subject to the action of
the greater force and move onward with the velocity correspond-
ing to the difference between the two forces.
Digitized by VjOOQ IC
170 Baron N. Schilling on the Constant Currents
Before we compare^ howeverj with one another the quantities
of these two forces, it will be necessary to illustrate further what
has been said, representing the earth in the plane of the meridian.
Let the circle P A S £ (fig. 5) be a terrestrial meridian, and
Fig. 6.
L the centre of the moon (or of the sun), which, as before, is on
the equator. The dotted Wnepase marks the form of the tidal
ellipsoid. Through the rotation of the earth the moon appa-
rently moves from east to west ; with it the ellipsoid /? a s e turns
about the axis P S, and develops, as we have seen, at the equator
two forces opposed one to the other. The one, the force effect-
ing the flood-current, directs its course from east to west, and
in the case here given is strongest at the equator, on which the
cusps of the ellipsoid move forward as long as the moon is on
the equator. This force will act in nearly the same direction on
both sides of the equator; only it must rapidly diminish as the
latitude increases; and in the latitude of the points nt, where
there is no rise of the water, the force acting from east to west
must be =0. Further polewards the tendency to form the
tidal ellipsoid may probably develop an inconsiaerable current
from the pole towards the equator, as shown by the lines p L
and s L.
The ebb-current force acts from west to east, as if the circle
pCsD revolved in this direction on the axis PS. As alreadv
said, it arises from the circumstance that all points in one half
of the earth are brought nearer to the moon by the rotation,
while all those in the other half are carried further from it. The
ebb-current force has its greatest intensity at the equator, and
diminishes very gradually on both sides of it, since the parallel
circles in low latitudes become only gradually smaller. Only in
high latitudes, where the circles diminish rapidly, does the force
of the ebb-current quickly diminish ; and only at the poles does
it entirely cease.
Since, as we have shown, the flood rises more above the nor-
Digitized by VjOOQIC
m the Air and in the Sea. 171
Dial level of the sea than the ebb sinks below it, we think we
can assume, as an hypothesis, that the force of the flood-current
will also be greater than that of the ebb-current.
In our case, if the cusps of the ellipsoid are on the equator,
and therefoie both forces develop their maximum on that circle,
the greater force must overpower the smaller, and both in air
and sea a current from east to west must prevail all along the
equator. On both sides of the equator the force of the flood-
current, acting from east to west, diminishes rapidly polewards;
the counteracting force of the ebb-current diminishes more
slowly. Therefore, at a certain distance from the equator, the
greater but rapidly diminishing force directed from east to west
will be only just as great as the smaller only slowly decreasing
force directed from west to east. In these parallels the forces, ba-
lancing each other, will generate no current. Still further pole-
wards the force of the flood*current, still continually more de-
creasing, will be less than that of the ebb-current, and, both in
the sea and in the atmosphere, currents from west to east will
make their appearance. In the latitude of the points m the
east-to-west force ceases entirelv ; while the opposite force has
in this latitude lost onlv a small portion (less than half) of its
action, and hence mav here produce a considerable current. In
higher latitudes the force of the ebb-current will also quickly
diminish, and the currents from the west become considerably
less, and their direction probably turn more towards the equator.
Accordingly, in the northern hemisphere, in high latitudes, cur-
rents will arise from the north-west, and in the southern from
the south-west.
TVlien, therefore, the moon and sun are at the same time in
the vicinity of the equator, a current in air and sea must flow
there from east to west. On both sides of the equator this cur-
rent will diminish polewards until it entirely ceases ; and there
must thus be produced a streamless zone parallel to the equator.
Further polewards a west-to-east current will prevail, which
must at first increase gradually until it attains its maximum ;
then will this current dso again diminish gradually, and in high
latitudes flow from the north-west in the northern hemisphere,
and from the south-west in the southern.
In reality we find this to be the constitution of the currents.
In middle latitudes constant west winds and sea-currents directed
eastwards prevail. In the latitude of about 80° there is in each
hemisphere a zone of no current, and in the tropical regions we
find currents flowing perpetually from east to west, both in air
and sea. An apparent exception is, that on the eouator we
meet with a zone m which no current is perceptible eitner in the
atmosphere or in the ocean.
Digitized by VjOOQ IC
172 BaroD N. Schilling on the Constant Currents
This circamstance seems at the first glance to contradict the
theory of the moon's attraction; yet the origination of this
equatorial streamless zone is easily explained when we reflect
that the moon and san are simultaneously in the vicinity of the
equator only for a very brief time twice yearly. They usually
describe parallel circles which lie between the equator and the
tropics ; the moon only goes sometimes slightly beyond the last-
mentioned circles. The ellipsoid arising from the united attrac-
tions of the moon and sun must always have its cusps between
the sun and moon ; and hence these cusps must mostly describe
parallels between the equator and the tropics.
Supposing the tidal ellipsoid in the position asep (fig. 6),
Fig. 6.
its major axis a e making a certain angle with the equator
A C E i)^ by the earth's rotation on its axis P S the cusps a
and e of the ellipsoid will describe the parallel circles a a! ^nd
eef } and therefore the maximum of the flood- current will also
be observed on these parallel circles. The current will also not
preserve its exact east- to- west direction^ but^ as shown by the
arrows B and F^ come from E.S.E. in the southern hemisphere,
and from E.N.E. in the northern.
On both sides of the parallel circles a d and e ff the force of
the flood-current will, as already said, diminish rapidly ; while
the ebb-current keeps, as before, the maximum of its force at
the greatest circle, therefore at the equator, and, also with this
position of the ellipsoid, diminishes only slowly polewards, con-
Digitized by VjOOQ IC
m the Air and in the Sea. 1 73
sequently will have already become slightly less at the parallel
circles al a and ef e, on which the maximum of the flood-carrent
is found. The direction of this current will also not be purely
from west to east, but, as the arrows C and D show, alternate
between W.N.W. and W.S.W. The opposite forces of the ebb-
and flood-current mast therefore on both sides of the parallel
circles a a' and e ef balance one another and form a zone of no
current.
This appears to occur in the vicinity of the equator and of the
parallels of 30^ latitude, the zones of calms and of the Sargasso-
seas being found there. In the latitudes of the parallel circles
a a' and ee! must be the maximum of the east-to-west flood-
current ; this perfectly corresponds with the phenomena of the
trade-winds and the equatorial currents. Polewards from the
streamless zone in the 30th parallel of latitude the rapidly dimi-
nishing force of the flood-current must be overpowered by that
of the ebb-current, and a constant current from west to east be
produced — which also actuaUy happens ; for between the 40th
and 50th parallels of latitude, or thereabouts, both in the air
and in the water, in all oceans and in both hemispheres, a cur-
rent directed eastwards is constantly observed.
Hence, it seems to us, the action of the attraction of the sun
and moon explains the origination of the trade- winds and anti-
trades with their zones of calms, and the rotation-currents run-
ning parallel with the equator, with the Sargasso-seas and the
streamless equatorial zone, considerably better than all hitherto
existing hypotheses.
If our explanation of the trade- winds and equatorial currents
is correct, also the position and the breadth of the current-zones
and the strength of the currents must themselves depend entirely
on the position of the tidal ellipsoid or on the position of the
moon and sun with respect to one another and relative to the
earth. When, for instance, moon and sun are both very near
the equator, the equatorial calm-zone must be non-existent, the
calms of the tropics must approach towards the equator, and the
constant west winds blow with greater force in lower latitudes.
Whether all this happens is unknown to us ; yet strong west
winds usually rage in Europe at the times of the equinox.
Just so, perhaps, it sometimes happens that ships cross the line
without calms ; but whether this chiefly coincides with the time
when the moon crosses the equator we know not.
When moon and sun are at the same time in the vicinity of
the tropics, the current-zones must be displaced polewards, and
the equatorial calm-zone be especially broad. It is possible that
then the ebb-current may predominate in the middle of the zone,
and that this circumstance accounts for the west-to-east current
Digitized by VjOOQ IC
174 Baron N. Schilling on the Comtani Currents
which flows in a narrow band along the equator and is named^
in Berghaus's 'Chart of the World/ the '' equatorial counter-
current/' In the air this current does not exist. It would
therefore have to be ascertained if this equatorial counter-current
is a constant one or is only to be observed when the moon ap-
proaches the tropics^ and whether it is not wanting when the mm
and moon are simultaneously in the vicinity of the equator.
The shifting of the trade-wind zones appears to be on the
whole more considerable than that of the sea-currents, and seems
in many cases to coincide with the change of the seasons of the
year — which, then, proves that the sun by its heat also exercises
an influence on the trade-winds. This probably takes place
chiefly through the sun's action on the aqueous vapour in the
atmosphere and through other collateral circumstances. The
main cause, however, of the production of the trade-winds must
certainly be ascribed to the attraction of the moon and sun ;
and hence their position relatively to each other must have a
sensible influence upon various atmospheric phenomena. It
appears, therefore, possible that the well-known old popular tra-
dition of the phases of the moon affecting the change of the
weather may have some foundation ; only it might be more cor-
rect to ascribe this influence not to the phases, but to the dis-
tance and declination of the moon, which latter, it is true, stands
in a certain connexion with the moon's phases and the sun's
declination. At the times, namely, of new and full moon the
difference between the declination of the moon and that of the
sun is always inconsiderable, although at the time of fuU moon
the sun and moon are in different hemispheres but at nearly
equal distance from the equator.
Only at the time of the quadratures can the difference of de-
clination of the sun and moon be considerable ; at the periods of
the equinoxes and the solstices the difference rises at the utmost
to near 28^
From the production of currents by the moon's attraction not
only can the sea-currents parallel to the equator, but also the
meridional currents be naturally derived.
If the whole earth were covered with water, the equatorial
current would flow round it unhindered ; but now the continents
stand as insuperable obstacles in the way of this motion. As,
however, the cause of the flow is not hereby removed, the cur-
rent in the ocean must continue and cannot suddenly cease on
impinging against the coast, but must change its dire^lion ac-
cording to the position of the shore. Thus we aae. in Ae
Atlantic Ocean, that the southern equatorial stream itvides at
Cape St. Boque (which opposes it Uke a wedge), and, following
the direction of the coast, is turned aside, part to the north-west
Digitized by VjOOQ IC
m the Air and in the Sea. 175
and part to the sonth-west. The north-west branch of this car-
rent unites in the Caribbean Sea with the northern equatorial^
and in this way impels almost the whole of the warmed water of
the surface of the Atlantic equatorial zone into the Gulf of
Mexico. The great mass of this warmer and therefore lighter
water driven together by the equatorial current must, of course,
have the tendency to spread over the colder and heavier water,
and to flow off northward. Thus arises, then, a current of warm
water flowing out of the Gulf of Mexico, commonly known by
the name of the Gulf-stream.
The motive force of the Gulf-stream musttherefoiebe derived
partly from the pressure of the equatorial current, partly from
the tendency of the warm water to spread over the cold of the
higher latitudes, but partly also from the attraction of the cur-
rent, directed eastward, of the middle latitudes ; but all these
causes spring directly from the attraction of the sun and moon,
which thus must be regarded as the prime motive force of the
Gulf-stream*.
The eastward current of the middle latitudes and the north-
east movement of the entire northern portion of the Atlantic
Ocean form the continuation of the Gulf-stream, and hence are
often designated by the same name — to which we have no ob-
jection, if it be kept in view that the prime cause of motion of
the two last-mentioned currents lies in the force of the ebb-cur-
rent. As already said, in about 30° latitude this force com-
mences to overpower the force of the flood-current, and develops
the maximum of its effect somewhere between the 40th and 50th
degrees of latitude ; farther polewards it diminishes considerably,
and becomes so feeble that it is no longer perceived as a current.
Nevertheless a slight movement eastwards appears to extend
considerably further towards the pole, and gradually to collect
the warmer water on the coasts of England and Norway. This
warmer water is derived partly from the Gulf of Mexico; but
part of it may have been heated on the surface of the ocean in
higher latitudes. The ebb-current, therefore, collects the su-
perficial warmer water in the eastern part of the ocean ; and the
tendency of the warm water to spread over the colder impels it
north-eastward, and thus accounts for the motion of the north-
ernportion of the Atlantic.
The principal force of the -ebb-current, flowing eastward, is
deflected south by the coasts of Europe, and, following the coast
of Africa, returns again into the equatorial stream. The attrac-
tion of the latter perhaps forms the principal cause of the south-
* Self-evidently it is not meant that the tan and moon's attraction heats
the water of the Gnlf of Mexico ; bat it is that which generates the equa-
torial current and thus odlects the warm water in the gnlf.
Digitized by VjOOQ IC
176 Baron N. SchilliDg cm the Constant Currents
ward bead, but may be assisted in some degree by the tendency
of the particles to move towards the equator^ produced by the
rotation of the earth. Only a small portion of the east-directed
current passes Cape Finisterre unhindered, and continues its
course in the natural direction along the north coast of Spain
till the coast of France compels it to curve sharply to the north-
west and follow exactly the course of the shore of the Bay of
Biscay, under the name of the Rennell current, to be lost at the
English coast in the general north-east current of the Atlantic.
The Rennell current shows distinctly how much power the
direction of coasts has to determine that of currents, even to
reverse their direction.
A portion of the South-Atlantic equatorial current turns to
the south-west from Cape St. Roque, along the coast of South
America. The impelling force of this Brazilian current is the
same as that of the Oulf-stream — partly the pressure of the
equatorial^ partly the high temperature of the water heated in
the Atlantic Ocean and collected at the coast by the equatorial
current, and partly the attraction of the eastward-directed ebb-
current fuiibtioning in the middle latitudes, into which the
greater portion of the Brazilian current passes to form the South-
Atlantic rotation-current. This latter, after crossing the ocean
from west to east, and having curved a little to the north, strikes
upon the African coast, and (for the same reasons as those above
discussed for the northern hemisphere) returns along it again
to the equatorial current, forming the South-Atlantic Guinea
current. The entire rotation-current, then, is originated by the
attraction of the moon and the sun, as this by its direct action
carries the water in the equatorial regions from east to west, and
in the middle latitudes from west to east, and hence also gene-
rates indirectly the currents flowing in the direction of the meri-
dian (the Gulf-stream and the North-African current, the Bra-
zilian and the South-Ouinea currents).
In the entire southern hemisphere all the cold polar currents
are directed north-east, which coincides perfectly with the action
of the moon's attraction in higher latituaes. Only in the north-
em hemisphere the directions of the cold polar currents contra-
dict the laws of the moon's attraction ; for the Greenland cur-
rent and the cold current of the Japanese sea have a south-west
direction, and not a south-east one, which they should have ac-
cording to our considerations. This, however, may well have
its cause in the action of the ebb-current, directed from west to
east, which gradually withdraws the warm northward-flowing
current from the coast ; and this is replaced partly by the cold
water of the bottom, but principally bv the less-salt and there-
fore lighter water derived from the melting of the ice. A similar
Digitized by VjOOQ IC
in the Air and in the Sea. 177
phenomeuoQ is often produced at coasts by the action of the
wind; and those who have sought a sea-bath will remember
that with a land-breeze the water is always colder than with a
sea-breeze. The former removes the warmed superficial water
from the coast^ by which the colder water beneath is brought to
light. The sea-breeze^ on the contrary^ drives to the shore the
water which has been warmed on the surface of the sea. WI at
the wind does in this case may well be brought about in a
higher degree by a permanent sea-current. In the depths,
even in the northern hemisphere, the polar currents appear to
be directed to the south-east. This is demonstrated by the
many icebergs which, near Newfoundland, cut through the
Gulf-stream in that direction. Dana^s chart of the isothermal
lines of the sea-surface in the coldest month^, on which the dis-
tribution of the corals is given, permits us also to draw a similar
conclusion. The polar limit of the coral zone, both in the
Atlantic and in the Pacific, is (probably on account of the water
being too cold) about lOP nearer the equator on the east side
than on the west side of the same ocean. It is interesting that,
according to this chart, the northern boundary of the corals is
10 degrees more to the north in the Pacific than in the Atlantic
Ocean. The reason is probably to be sought in the fact that the
Atlantic forms almost the only discharge^ and the main supply,
of the north polai' basin.
The alternating warm and colder strips of water in the Gulf-
stream, as well as in the Kurosiwo, seem to us to favour the
idea that the force which carries away from the coa^t the entire
current eastwards is not constantly of equal strength, but, so to
speak, has a reflex action — which perfectly corresponds with our
hypothesis, according to which, in the middle latitudes, the force
of the ebb-current must on the whole take the upper hand, but,
through the westward-directed force of the flood-current, may
be subject Co periodical interruptions.
L. von Schrenk, Member of the Academy of Sciences of St.
Petersburg, has recently, in a very interesting work [StrdmungS'
Verhalinisse im Ochotskischen und Japanischen Meere), pointed
out that in the Yellow, as well as in the Japanese and partially
in the Ochotsk Sea^ the temperature of the water is constantly
lower at the east coasts of the continent and the islands than at
the west coasts. We see in this a proof that in these inland seas
there is the same tendency of the water to move eastwards, and
that thereby the upper warmer water is accumulated at the east
side of the sea or at the west coast of the land. In the
White Sea also, and the Varanger Fjord in North Lapland^
the temperature of the water is higher in the eastern parts than
* Stieler'B Hand-Atlas, 1867, No. 9, Cartoo.
Phil. Mag. S. 4. Vol. 48. No. 317. Sept. 1874. N
Digitized by VjOOQ IC
178 Baron N. Schilling on the Constant Currents
in the western. As we have already remarked, the warmer
water accumulated on a coast must flow away polewards, while
the cold water of the west side of the sea seeks to occupy the
space left free, and so flows towards the equator. It is also in-
teresting that Schrenk^ has pointed out the existence of strips
of cold water in the warm current of the Japanese Sea. The
colder but very slightly less salt water may, under some circum-
stances, have exactly the same specific gravity as the warm,
somewhat salter water; and hence they may flow a long time
side by side without mingling. These strips of colder water
have not yet been demonstrated in the Brazilian and Mozam-
bique currents ; but it is probable that they are present there
also, especially in the Brazilian current, which extends further
south. Indeed it is likely that these warm currents are sepa-
rated from the coast by colder water.
The Mozambique current, it seems to us, strikingly corre-
sponds with the theory of the moon's attraction. It has its
origin in the equatorial stream of the Indian Ocean, then foU
lows the east coast of Africa in a south-westerly direction,
and, still foUowiug the coast, at the southern extremity of the
continent takes a westward direction, but thereby comes into
the region of the ebb-current and at once, with a remarkably
sharp bend, returns eastward. We can only account for this
sudden flexion by the action of the moon^s attraction ; for it
is impossible to admit that the aspirating force of the Indian
equatorial stream can occasion this sudden bend in order to
carry the Mozambique current to the shores of Australia and
New Zealand. Moreover the depth to which the constant
ocean-currents extend appears to us to be explicable only by
the attraction of the moon and the sun ; for it acts on all
the water-particles as far as the bottom of the ocean, if its
action below is slightly less than its action above. The cur-
rents of the remaining oceans are so perfectly similar to those
above discussed, that in describing them we should have to
repeat nearly the same things. They are all originated prin-
cipally, either directly or indirectly, by the action of the flood-
and ebb-currents, and hence can only be satisfactorily explained
by that action.
The currents of the atmosphere rest at all events upon pre-
cisely the same laws ; but air-currents are far more susceptible
to all possible collateral causes than ocean-currents, and are
therefore subject to many other influences, amongst which dif-
ference of temperature plays a certain part. Unfortunately this
influence has hitherto been considerably overrated; for polar
and antipolar currents generated by difference of temperature
* Op. cit. p. 66.
Digitized by VjOOQ IC
in the Air and in the Sea. 179
have been regarded as the basis of meteorology, or as currents
on which all the movements of the air depend. To this opinion
we cannot assent ; on the contrary, we believe that in the atmo-
sphere, just as in the sea, the principal motions take place in
directions nearly parallel to the equator.
Perhaps, in the future, with more accurate knowledge of the
action called forth by the attractions of the sun and moon, we
shall succeed in explaining the causes of rotatory storms by the
two opposite directions of the flood- and ebb-current. May
not in certain cases, at the time of the quadratures, the ebb-cur*
rent caused by the moon meet at a certain angle the flood-cur-
rent called forth by the sun and thereby produce the rotating
motion f Up to the present time the important natural pheno-
menon of cyclones has by no means been explained; for all
hitherto-given explanations have been quite inadequate.
As is known, these storms always have two motions — one
rotating, and one progressive. The progressive motion corre-
sponds well with the theory of the moon's attraction ; for these
storms almost always commence in low latitudes, and, in both
hemidpheres, the centre of the storm moves westward in the
region of the flood-current, at the same time slightly increasing
its distance from the equator and thereby arriving m the calm-
zone of the tropic. Here the velocity of the progressive motion
becomes cqnsiderably less, and its course makes a sharp curve
eastward, the hurricane passing into the region of the ebb-cur-
rent; and now, in both hemispheres, it moves with great velo-
city to the east and somewhat polewards. Therewith its dia-
meter gradually increases and the circular motion diminishes
until the hurricane is lost in higher latitudes. The usual dura-
tion, from beginning to end, of the hurricane is about 14 days.
The rotating motion of these storms is subject to quite deter-
minate but not yet discovered laws. In the northern hemisphere
they rotate in the opposite direction to that of the hands of a
cluck ; but in the southern hemisphere they go round in the
same direction as the latter. In other words, in both hemi-
spheres the storm always blows from the west on the side to-
wards the equator, and from the east on the polar side. West-
wards of the centre of the hurricane, the direction of the storm
is always to the equator ; eastward of the centre, away from the
equator; so that hurricanes rotate in an opposite direction to
the cuiTcnts of the seas. Ordinary storms appear to stand in
the closest connexion with cyclones ; at least this conjecture is
corroborated by Buys-Ballot's law, according to which the winds
revolve about the minimum of atmospheric pressure in the same
direction as the cyclones.
The explanation that the rotating motion of cyclones arises
N2
Digitized by VjOOQ IC
180 Prof. Challis on the Hydrodynamical Theory of the
from the rotation of the earth is altogether inadmissible ; for
the hurricane always commences in very low latitudes^ with a
diameter which seldom occupies more than 2 or 3 degrees of
the meridian. The difference in magnitude of the parallel
circles^ however^ i^ so inconsiderable that the air streaming to
the centre can only be deflected by the earth's rotation to an
angle of 2 or 3 degrees from the meridional direction. As-
suming that the centre of the cyclone is^ at the beginning of the
hurricane, in 10^ latitude, that its radius occupies 2 degrees of
the meridian, and that the air requires two hours in order to
traverse this distance, and retains during the whole time the
rotation-velocity of the parallel circle which it has left behind,
in this case the air- particles from the 12th degree of latitude,
streaming to the centre of the hurricane, would deviate a little
to the west from the meridian, forming with it an angle of 2^45'.
Those from the 8th degree of latitude, streaming to the centre,
would deviate eastwards, their direction forming with the meri-
dian an angle of 2^ 21'. But this much too small deviation
from the meridian cannot possibly occasion the rapid whirling
motion of the storm.
Not doubting that such a theory of the ocean-currents and
the trade-winds, founded on the attraction of the moon, may be
the correct one, we nevertheless acknowledge how much our view
needs to be subjected to further elucidation. Time must bring
a multitude of fresh observations before the special authorities
can have spoken their last word on this subject. To us, how-
ever, it will afford the fullest satisfaction if we have had the
good fortune, by the foregoing analysis of our views, to contri-
bute, at least indirectly, to the advancement of this department
of physical geography, which has hitherto wanted a uniting fun-
damental idea.
XXIX. The Hydrodynamical Theory of the Action of a Galvanic
Coil on an external small Magnet, — Part I. By Professor
Challis, M.A., F.R.S.*
1. rr HE mathematical theories of the physical forces which I
-L have published from time to time in this Journal have
been made to rest exclusively on the following hypotheses : — All
visible and tangible substances consist of inert spherical atoms
of constant magnitude, and all physical force is either mode of
pressure of the aether on the surfaces of the atoms, or reaction
of the atoms at their surfaces due to the constancy of their form
and magnitude. The sether is supposed to be a continuous
elastic substance, filling all space not occupied by atoms, of
• Communicated by the Author
Digitized by VjOOQ IC
Action of a Galvanic Coil on an external small Moffnet. 181
perfect fluidity, and of the same density every where when at
rest, and when in motion varying in density always and at ali
points in exact proportion to variations of its pressure. Also
the size of the atoms is supposed to be so small that even in
dense bodies they fill a very small portion of a given space.
2. These hypotheses, which I have enunciated on several pre-
vious occasions, are repeated here for the purpose of directing
attention to what especially characterizes them. They involve
no assertiun that is not comprehensible by the indications of com--
mon sensation and eaiperience. It is because they possess this
character that the physical theories I have founded on them
differ from those generally maintained by contemporary physi-
cists, which rest for the most part on experimental data con-
ioined with arbitrary hypotheses not in the same manner intel-
igible. It does not, however, follow from the dissimilarity of
the hypotheses that the two modes of philosophizing are con-
tradictory to each other. This I think I shall be able to show
by pointing out the distinction between their fundamental prin-
ciples, and the consequent relation in which they stand to each
other.
3. For this purpose reference will be more particularly made to
the physical theories of magnetism and galvanism, as proposed
by Gauss and Ampere, or illustrated and extended by other
physicists who have adopted their views. The object of all in-
vestigations of this class is to deduce from the results of certain
fundamental experiments, by the inter\'ention of arbitrary or
provisional hypotheses, mathematical expressions of the laws of
the phenomena. Accordingly natural philosophy is not thereby
advanced beyond a stage analogous to that to which physical
astronomy was brought by the results of Kepler^s observations.
Newton*8 hypothesis of a gravitating /orc^ varying inversely as
the square of the distance, and his discovery of the mode of cal-
culating its effects by mathematics, were steps necessary for
completing that science, inasmuch as they gave reasons for
Kepler^s laws. In the empirical theories I am referring to, the
consideration of physical force is included, and from certain
hypothetical modes of action of the forces mathematical expres-
sions of the laws of the phenomena are deduced. But con-
fessedly the intrinsic nature of the forces, and the reasons for
the facts and hypotheses on which the investigations rest, ai*e
left undetermined.
4. The final stage of physical investigation is reached when
explanations of phenomena and of their laws have been given by
means of mathematical deductions from hypotheses satisfying
the condition of being intelligible from sensation and experience.
Till this is done, we can hardly be said to have arrived at theory
Digitized by VjOOQ IC
182 Prof. Challis on the Hydrodynamical Theory of tlie
properly so called. The antecedent steps of theory ought, for
distinction, to be called empirical or provisional^ as resting on
arbitrary hypotheses, and as subsidiary to true and complete
theory. True theory rests on hypotheses that are not only com-
prehensible^ but also ultimate and necessary — that is, such as do
not admit of being accounted for by any ulterior hypotheses.
This will be proved to be the specific quality of the hypotheses
stated above (art. 1), if they should be shown to be adequate to
the explanation of the nature, laws, and consequences of the
operation of all the different kinds of physical force. To de-
monstrate their adequacy for this purpose has been the express
object of the many theoretical researches I have been occupied
with relative to the modus operandi of physical force generally.
This course of philosophy I propose to call Newtonian, its
*' foundation ^' having been indicated by Newton in the Third
Book of the Principia. (See the discussion of this view in the
Philosophical Magazine for October 1863, p. 280.)
5. Having thus pointed out that a distinction is to be made
between empirical theory resting on arbitrary hypotheses and
ultimate theory resting on strictly a priori hypotheses, I have
further to state in what respect the two kinds of theory may be
considered to be related to each other. Let it be supposed that by
means of a theory depending on certain ascertained facts, and on
hypotheses thereby suggested, a true mathematical expression
of the laws of the phenomena proposed to be accounted for has
been obtained. According to views entertained by some theo-
rists of the present day, natural philosophy consists in thus
arriving at phenomenal laws, and there is no occasion for any
further investigation. But the principles of the philosophy I
call "Newtonian^' demand that the explanations of all phe-
nomena and their laws should be inferred by mathematical rea-
soning from the before-mentioned fundamental hypotheses.
Now this may be done in two ways — either directly, by in-
dependent deductions from the a priori hypotheses, or inter-
mediately, by deducing from the same hypotheses explana-
tions of the facts and hypotheses which form the basis of a
true empirical theory. It is evident that in either way the phe-
nomena are shown to be consequences of the operation of intel-
ligible causes, and are completely explained. It appears thus
that the empirical method is subsidiary to the h prioii method
whenever the explanation of phenomena is effected by the aid
and intervention of the former, and that in this respect the two
methods may be mutually related. These remarks will receive
elucidation in the course of the subsequent discussions.
6. I propose, in the first instance, to give an h priori expla-
nation of the facts relating to the action of a large magnet on a
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Action of a Galvanic Coil on an external small Magnet, 183
small needle from whicb^ by the intervention of certain arbitraiy
hypotheses, Gauss inferred the law of the inverse square in mag-
netic action. For this purpose it will be convenient to refer to
the detailed exhibition of Gauss's argument given in the Astro-
nomer Royal's ' Treatise on Magnetism ' (Macmillan and Co.,
1870). I have already discussed this question on hydrodyna-
mical principles in a " Note on the Hydrodynamical Theory of
Magnetism '' contained in the Philosophical Magazine for July
1869, to which I beg to refer for details of the mathematical
reasoning relating to the physical conditions of magnetic force.
I propose to reproduce here only so much of that discussion as
may be required for understanding the subsequent theory of the
action of the galvanic coil on a small magnet, which is the ulti-
mate object of the present communication.
7. In the article just referred to it is assumed that in a mag-
netized bar there is a small and regular increment of atomic
density from end to end, like that which must be produced by
the action of gravity from the top to the bottom of a solid or
fluid mass resting ou a horizontal plane. In a '' New Discus-
sion of the Hydrodynamical Theory of Magnetism,'' contained
in the Philosophical Magazine for June 1872, 1 have proved (in
arts. 4-9) that if any body in which such gradation of density
exists be traversed either by a steady setherial stream, or by a
uniform series of undulations of the sether, a secondary steady
stream will be produced by impulses continually given to the
fluid in the direction from the rarer to the denser parts of the
body, this being the direction of the contraction of channel
by the occupation of space by the atoms. The application of
this result forms an essential part of the hydrodynamical the-
ories of electric and magnetic attractions and repulsions which
I have proposed and discussed in several previous communica-
tions. In the case of a magnet^ the gradation of atomic density^
when once induced, subsists independently of the action of an
external body, and is consequently maintained by the intrinsic
molecular forces of the magnet itself. Accordingly I have as-
sumed that whereas in general the molecular attractions acting
on a given atom in equilibrium counteract each other, as do
also the molecular repulsions, in the case of a magnetized steel
bar the equilibrium of the atom results from an equality between
the molecular attraction towards the denser end and the mole-
cular repulsion towards the rarer end. This, in short, is con-
sidered to be the distinctive property of a substance suscep-
tible of being magnetized. Steel possesses this property in an
eminent degree, and can be permanently magnetized. Soft
iron admits only of temporary magnetization.
8. The magnetic state of a substance being thus defined^
Digitized by VjOOQ IC
18i Prof. Challis on the Hydrodipiamical Theory of the
and its magnetic action being supposed to be attributable to
the setherial streams which^ as indicated above^ this state ge-
nerates when the substance is traversed either by steady streams
or a uniform series of vibrations^ we have next to inquire re-
specting the origination of these primary movements of the
ffither. I thought^ at firsts they might be due to the sethe-
rial streams which relatively pass through atpmically constituted
substances in consequence of the earth's revolution about its
axis and motion in its orbit^ and of the motion of the solar
system in space. But since in that case the primary^ and by
consequence the secondary^ motions would be subject to large
fluctuations of intensity to which there is nothing corresponding
in the phenomena of a magnet^ it follows that the streams which
are the exponents of magnetism cannot be to any sensible
amount due to the above-mentioneil primaries^ and must have
a different origin.
9. Having proved^ as stated in art. 7, that the secondary
streams might be generated by a uniform series of setherial un-
dulations^ and having repeatedly maintained (in articles in the
Philosophical Magazine and in my work on the Principles of
Physics) that attractions and repulsions may be attributed to
the dynamical action of such undulations on the individual
atoms of bodies, it occurred to me that those vibratory motions
of the sether which by their attractive effect maintain the regular
gradation of density might be the primaries sought for; and
this supposition is in accordance with the fact already adverted
to, that magnetism pertains to the magnetized body apart from
any extraneous action. [See^ respecting '^ Attraction by Vibra-
tions of the Alt" an article in the Philosophical Magazine for
April 1871. I cannot but regard the results of Mr. Guthrie's
experiments as singularly confirmatory of my theoretical anti-
cipations.] According to the views I have advocated relative to
molecular forces, the maximum velocity of the attractive vibra-
tions would be so much larger than that of the repulsive vibra-
tions, that in the present inquiry the latter may be left out of
account. Also it may be presumed that it is because that
maximum velocity very much exceeds the rotatory^ orbital, and
translatory motions of the earth, that these motions have com-
paratively no magnetic effect.
10. Consequently, if, for simplicity, the magnet be supposed
to be of a cylindrical form, in its interior an impulsive action
upon the sether is continually operating in the directions parallel
to its axis. Now as the attractive action of a series of undula-
tions is in the direction contrary to that of propagation, and the
attraction is towards the denser end of the magnet, it follows
that the direction of the propagation, which is that of the maxi-
Digitized by VjOOQ IC
Action of a Galvanic Coil on an external small Magnet. 185
mum velocity in the condensed half of the wave, is towards the
rarer end. At the same time, according to the mathematical
result obtained in art. 8 of the article in the Philosophical Ma-
gazine for June 1872, the impulsive action on the sether, whether
the primary vibratory motions be backwards or forwards, is
towards the denser end, out of which consequently the generated
streams flow.
11. The next point is to determine the forms of the courses
of the magnetic streams generated under the above-described
circumstances. To do this it is necessary to begin with admit-
ting the truth of the following general hydrodynamical theorem,
of which great use will be made in the subsequent investiga-
tions. [For proof of the theorem see art. 10 of the communi-
cation just cited.] It is not possible that the motion of an un-
limited fluid mass can be such as to transfer any portion of the
fluid on one side of an unlimited fixed plane to the other side
without the transfer of an equal portion from the latter to the
former. Thus the motion must be circulating or reentering \
and accordingly a general characteristic of magnetic and gal-
vanic currents is accounted for on the principles of hydrody-
namics.
12. This being understood, the forms of the magnetic linen
of motion are determinable, at least approximately, by the fol-
lowing argument. We have seen that in consequence of the
regular gradation of the atomic density of a cylindrical magnet,
and the velocities due to the outstanding undulations which by
their attractive action maintain this state of density, the fluid is
impelled in each transverse section at every instant towards the
denser end of the magnet. These impulses operating against
the inertia of the surrounding mass of fluid, have the effect of
generating streams which, as being due to a steady action, are
steady, and^ as fulfilling the condition stated in art. 11^ are ne-
cessarily circulating. To give a first idea of the courses of these
streams, at least in the immediate neighbourhood of the mag-
net, I cannot do better than refer to the figure in p. 17 of the
Astronomer RoyaFs ' Treatise on Magnetism,' the directions of
the axes of the small magnets indicating (as will be shown sub-
sequently) the directions of the lines of motion at the positions
where they are situated. An approximate analytical expression
for the forms of these magnetic curves is derivable from the pre-
sent theory by the following investigation.
13. From what is argued above, the impulses are produced
by variations of pressure due to variations of the square of the
mean of the velocities within the cylinder estimated in directions
parallel to its axis, these variations being caused exclusively by
the mean contraction of channel resulting from the increasing
Digitized by VjOOQ IC
186 Prof. Challis on the Hydrodynamical Theory of the
occupation of space by tbe atoms towards the deuser end. Now
we may conceive this mean eflFect to result from the separate
effects of a vast number of atoms contained within a thin trans-
verse slice of tbe cylinder, inasmuch as the individual motions
due to the occupation of space by the atoms may coexist^ and
the parts of the motions resolved transversely to the axis will in
that case destroy each other. Also it is to be considered tliat
the motions of the aether resulting from the mean of the impulses
must satify the condition of circulating.
14. This being understood, it will be seen to be allowable
to substitute for the impulsive effect of contraction of channel
that of a motion forward in the same direction of the aggre-
gation of atoms contained in the above-mentioned slice, the
fluid being relatively at rest. For on this supposition there
will be a mean impulse parallel to the axis of the cylinder^
which will be the sum of the impulses of the individual atoms
resolved in that direction, and moreover will give rise to a
drwlating motion. The last assertion rests on Poisson^s so-
lution of the problem of the simultaneous motions of a ball-pen-
dulum and the surrounding fluid, according to which the lines
of motion of the fluid are reentering ; and this being the case
with respect to each atom, the result of the composition of all
the motions will be circulating motion. Now, assuming the
transverse section of the cylinder to be small, it is evident
that the stream resulting from the action of all the atoms in
the slice will have quum proxime the same form as that pro-
duced by a single atom situated at the middle point of the slice.
But by Poisson's solution we obtain the analytical expression
of the motion of the fluid in this case. Hence a formula for
expressing the motion due to all the atoms in a given small
slice may be at once inferred.
15. Let A and B be the extreme points of the axis of the
cylinder, 0 its middle point, P any extraneous point the coor-
dinates of which reckoned from 0 along and perpendicular to
the axis are p and g, and Q being a point of the axis distant by
X from O ; let the straight line joining P and Q make an angle 6
with the positive direction of the axis. Then if PQar, /a be
the velocity of the atom, and a its radius, by the above-men-
tioned solution the velocity at P in the direction from Q to P is
^ cos 0, and that perpendicular to P Q tending in the negative
direction is —-g sin 6. Hence, denoting by X and Y the total
velocities resolved along and transversely to the axis, we have
^= ^ cos« tf- ^sin« tf, Y= ^%08 0 sin 0+ ^sintfcos^:
Digitized by VjOOQ IC
Action of a Galvanic Coil on an external small Magnet. 187
or, since cos 0=^ , sin ^= -, and r^= [p—xY + q^,
x^aefi jLPz:?)*±i?!_ Y=: ^f^'^^Jp-^)
Hence^ to calculate the total velocity at P in the longitudinal
and transverse directions, we have to add the velocities due to
all the slices of given thickness dx from end to end of the mag-
net, or to obtain the integrals k^Xdx and k^Ydx from a?= — /
to a?= + /, the length of the magnet being 21, and * a constant
factor. The results will be found to be
Longitudinal^ _ k^ut^ f p-^l P±i__\
velocity J 2 L((j»-/)« + ^«)J ((;? + /)* + ^«)? J '
Transverse \ _ J^f g q \
velocity / 2 L(g«+(p-/)«)f (g« + (;, + /)«)* /•
16. It will now be shown that these velocities are propor-
tional to the directive actions of the magnet in the longitudinal
and transverse directions on a small needle having its centre at
P, and movable about an axis perpendicular to the plane con-
taining P and the axis of the cylinder. The small magnet will
be supposed to be surrounded by magnetic streams exactly like
those which, according to the foregoing theory, belong to the
large magnet, and to be of such small dimensions that the
streams from the large magnet may be considered to have the
same direction and velocity at all the positions of the atoms of the
other. To find the action of the large magnet on the small one,
it is now required to determine for any point the accelerative
action of the pressure of the fluid resulting from the coexistence
of the two sets of motion.
1 7. It is clearly not necessary to take account of any force
acting* perpendicularly to the plane passing through P and the
axis of the cylinder, because all such forces are equal and oppo-
site on the two sides of the plane. Let, therefore, that plane
contain the axes of a? and y, and let u„ t7. be velocities, parallel
to the axes, due to the large magnet, ana t^ v^ be those due to
the small one. Then by hydrodynamics, the motion being
steady, and, as vanishing at an infinite distance, such as makes
udx+vdy+wdz an exact differential, we have
p=C-i((tt,+«,)«+K4r^«)-
Let V, be the velocity of the incident stream of the large mag-
net, and let its direction make an angle ^^ with the axis of x.
Then Wj=Vi cos ^, and t?j=Vj sin ^,. Again^ let the velocity
Digitized by VjOOQ IC
188 Prof. Challis on the Hydrodynamical Theory of the
of the small magnetos stream at the position of any one of its
atoms be V,, and be in a direction making the angle a with the
axis of the magnet, and let this axis make the angle 6^ with the
axis of X, Then we have
UgSsV^cos (^g—a), Va=V2 sin (^g— «).
Hence, by substituting in the above expression for p,
;,=C«i(VJ + 2V,V4C0S (^^-^, + a)-hVj).
The pressure /?, so far as it depends on the term VJ, can have
no effect in producing either rotation or motion of translation of
the small magnet, because the velocities Vj are symmetrical
both with respect to its axis, and to the transverse plane passing
through its centre. Hence, omitting this term, we have, since
y^ and 9, have been supposed constant, and 0^ is a constant
angle,
^P -tr /zi /ivrf.VaCOSa „ . .^ /j.rf.VflSina
- £ = V, cos {0,-0^) —^ V, sin {0,-0^ j—- i
SO
^P -ir //J /jvrf.VoCOsa ,, . .^ yjvrf.Vasina
- fy = V. COS {0,-0^) —1^ V, 8.n {0,-0,) —^-
18. We may now simplify the reasoning, without loss of ge-
nerality, by supposing that the axis of x coincides with the axis
of the small magnet, or that d^=^0. In that case S .— ^p =0,
ax
because by reason of the symmetry of the motion the positive
values of J are just counteracted by the negative, and
the same is the case with respect to the values of — ^ V — •
Hence the forces parallel to the axis of the magnet have no ten-
dency to produce motion of translation. Neither do they tend
to produce rotation, because corresponding to a force at any
point on one side of the axis there is an equal force at an equal
distance on the other side, and equally distant from the axis of
motion. We have thus only to consider the effects of the forces
- ^. Now the sum of these forces is zero, because by reason
of the symmetry of the motion, the sums of the positive values
.^.V^cosa jd.V-sina . , i ^ ^i.
oi ^ and ^ are respectively equal to the sums
of their negative values. Hence there is no tendency to motion
of translation transversely to the axis. Also the forces expressed
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Action of a Galvanic Coil on an external small Magnet, 189
by the different values of the first term of the formula for r-
produce no motion of rotation^ because they are equal and in the
same direction at equal distances from the axis of rotation on
the same side^ whether positive or negative^ of the axis of the
magnet.
19. But the forces expressed by the second term of the same
formula are at a given distance from the axis of motion equal
and in the same direction at points equally distant from the axis
of the magnet on opposite sides, and at the same time the direc-
tions are opposite on the opposite sides of the axis of motion.
Accordingly these forces produce motion of rotation, and are
the only forces that have this effect. Hence if x^ be the distance
of any atom from the axis of rotation, the whole momentum of
rotation is propoitional to
TT • zi ftx? rf.VflSina
— V, sin ^1 X 22 . X. 5 >
dy
the summation embracing all the atoms on one side of the axis
of rotation. It is now to be considered that the accelerative
action of the fluid in steady motion on any atom in any direction
has a constant ratio to the accelerative force in the same direc-
tion of the fluid itself at the position of the atom. [This pro-
position is proved in pp. 313-315 of * The Principles of Mathe-
matics and Physics.'] Hence, if H be a constant factor having
a certain ratio to the result of the above summation, the directive
force of the incident current will be
HVisin^,,
tending always to place the axis of the small magnet in such a
position that its proper current along the axis and the incident
current flow in the same direction, in which case d|=0.
20. *It follows from the foregoing argument that the longitu-
dinal and transversal components of a stream from a large mag-
net incident upon a small one are proportional to the directive
forces of the stream in th#two directions, and that consequently
the forces may be supposed to be expressed by the formula for
the velocities obtained in art. 15.
I take occasion here to remark that the Astronomer Royal
has deduced in the Philosophical Transactions (vol. clxii. p. 492)
expressions for the same forces wholly different from those in
art. 15, by assuming the intensity of the magnetism along the
axis of a magnet to vary proportionally to the distance from its
centre, and finds that they give numerical results which do not
sufficiently agree with experiment. According to the theory I
am advocating that assumption is not allowable.
Digitized by VjOOQ IC
190 Prof. Chailis on the Hydrodynamical Theory of the
21. I proceed now to account by the hydrodynamical theory
for the experimental facts on which the Gaussian argument for
the law of the inverse square in magnetism rests. In one set
of experiments the small magnet was placed so that the prolon-
gation of the axis of the large magnet passed through its centre
and cut its axis at right angles. Under these circumstances the
ordinate ^=0^ so that the transverse velocity vanishes^ and the
expression for the longitudinal velocity becomes
kfic^f 1 1 \
2 \{p-l)^ {p^l)V'
which, if the ratio of I top be small, is very nearly
In another set of experiments the small magnet was placed
with its axis pointing to the centre of the large one transversely
to the axis; in which case^ since /?=0^ the transverse velocity
again vanishes^ and^ supposing the ratio of / to g to be small^
the approximate expression for the longitudinal velocity becomes
Hence in both cases the directive force varies inversely as the
cube of the distance from the centre of the large magnet, and at
equal distances is double in the former case to what it is in the
other. The two principal results of the experiments having
been thus accounted for, the hydrodynamical theory has effected,
at least to a first approximation, all that may strictly be de-
manded from it. In order, however, to exhibit its applicability
more fully, I shall now employ it to show why Gauss's empirical
theory succeeds in representing the same facts.
22. It has been inferred from the hydrodynamical theory that
the action of the large magnet on the small one is simply directive*
Hence, assuming that each magnet has near its ends a positive
pole and a negative pole, and that like poles repel each other
and unlike poles mutually attract, it will readily be seen that,
according to the arrangements of the two experiments described
in art. 21, the actions on the poles of the small magnet are nearly
equal, and nearly in the same direction, and that the action on
one is attractive and that on the other repulsive. These forces
are, therefore, proper for acting as a kind of cotgple, and giving
direction to the axis of the needle. Also in this mode of viewing
magnetic action, if, as is empirically assumed, the force varies
inversely as some power of the distance from the pole, the law
of the inverse square is alone applicable, because experiment and
the hydrodynamical theory concur in indicating that the direc-
Digitized by VjOOQ IC
Action of a Galvanic Coil on an external small Magnet. 191
tive force varies nearly as the inverse cube of the distance from
the centre of the magnet^ which law results from the joint action
of an attractive and a repulsive force expressed thus.
{r-\-Br)'*
9 ^
the differential force being nearly -^— , which for a given value
of Br varies inversely as the cube of the distance.
23. The whole preceding argument points to the conclusion
that the assumed attractive and repulsive magnetic forces have
only a hypothetical existence, and that what really exists is hy-
drodynamical pressure.
24. Proceeding now to discuss in a similar manner the pro-
blem of the action of a galvanic coil on a small magnet, I propose,
first, to solve it according to the principles of the hydrodyna-
mical theory of galvanism, and then to inquire how far the same
theory will account for the facts and hypotheses on which Am-
pere's empirical solution of the problem rests. The hydrodyna-
mical considerations will differ in some essential respects from
those applicable to magnetism.
25. First it will be necessary to ascertain what motions of the
fiether correspond to the transmission of a galvanic current along
a fine wire. For this purpose certain hydrodynamical theorems
will be employed, the principles and the proofs of which I have
discussed in various antecedent researches. I consider it to be
an axiom that^ whatever be the motion of a fluid mass, the lines
of direction of the motion may at all times be cut by a surface
made up of portions, either finite or indefinitely small, of differ-
ent surfaces of continuous curvature, so joined together that the
tangent planes at the points of junction of two contiguous por-
tions do not make a finite angle with each other. The reason
for the latter condition is a dyrmmical one, whereby infinite forces
are excluded. The other is an abstract geometrical condition of
continuity, to which the directions of the motion of a fluid
assumed to be continuous are necessarily subject, and in virtue of
which the motion admits of being calculated. If any one thinks
that there are motions of a fluid which this condition does not
embrace, let him calculate them if he can ; I do not concern
myself with them.
26. It follows from the foregoing theorem that the general
differential equation of the above-defined surfaces of displacement
is (according to the usual notation) udX'\-vdy-\-wdz^O, and
that consequently the left-hand side of this equality is either in-
tegrable of itself or by a factor. Reasoning on the principle
that this must be the case always and at ail points of the fluid.
Digitized by VjOOQ IC
192 Prof. Challis on the Hydrodynamical Theory of the
I have obtained a general hydiodyuamical equation in which the
factor enters as an unknown quantity. The present investiga-
tion does not require reference to that equation further than to
state that it serves to demonstrate the reality of the factor^ and
consequently to establish the truth of the equation
/dv dw\ , fdw du\ . rdu dv\ ^ , .
which^ as is known^ is the general expression of the condition that
udx 4- vdy + wdz is integrable by a factor.
27. I have recently learnt with some surprise from more than
one quarter that the equation (a), and^ by consequence^ the an-
tecedent views on which it is founded, are considered to be untrue
for reasons drawn from a discussion on certain hydrodynamical
questions which I had with Professor Stokes in the Philoso-*
phical Magazine so long ago as 1842. Claiming to adopt views
expressed by Professor Stokes on that occasion, a correspondent
sends me the following argument relative to the equation [a).
Conceive to be impressed on all parts of the fluid the arbitrary
constant velocities a, ^, 7 in the directions of the axes of coor-
dinates. Then the equation becomes
, . .fio dw\ . , as fdw du\ . . .fdu dv\ ^
which, since a, ff, 7 are perfectly arbitrary, cannot be true unless
dv ^^_n ^^ ^" ~n ^" ^^ —A.
dz dy^"' dx dz '^ ^ dy dx~ ^
that is; unless in every instance of the motion of a fluid
udx^vdy-\-wdz is an exact differential. As this is certainly not
the case, it is concluded that the equation (a) is untrue.
28. The answer to this argument is that the equation (a) was
deduced on the principle of its being exclusively applicable to mo-
tions which are peculiar to a fluid, and which, consequently, a
solid is not capable of, the motions, namely, by which the parts
of a fluid mass in motion can change their relative positions.
This is the sole raison d'etre of the equation. Hence the intro-
duction of the velocities a, jS, y common to all the parts of the
fluid is a violation of the principle on which it is founded ; or
rather the above argument is a proof h posteriori that the equa-
tion excludes such common velocities. If, therefore, that equation
be satisfied, there is no need to '^ define ^' the velocity that may
be common to all the parts of the fluid ; for either such motion
takes place under given conditions, and is consequently known,
or, if not known and not knowable (whether it be due to the
earth^s rotatory and orbital motions^ or to the motion of the
Digitized by VjOOQ IC
Action of a Galvanic Coil on an external small Magnet, 193
solar system in space) ^ the determination of the motions whereby
the individual parts of the fluid alter their relative positions
remains the same.
29. If while such change of relative position is taking place
each rectangular fluid element is also changing form^ the lines
of motion are necessarily not parallel ; an(i since^ by hypothesis^
they are in the directions of normals to continuous curved sur-
faces, it follows that for such motions v>dx-\-vdy + wdz is an exact
difierential. But if each rectangular element retains the same
form^ the lines of motion must be parallel^ the surfaces of dis-
placement are planes, and udx+vdy-k-wdz is integrable by a
factor.
In the course of my many hydrodynamical researches I have
had from time to time the benefit of criticisms^ and arguments
ex adverso, from my mathematical contemporaries ; and I wil-
lingly admit that I have thereby been induced in several instances
to modify my original views. But hitherto I have not perceived
that there is any ground for questioning the truth of the prin-
ciples and the reasoning which have conducted me to the equation
which I call the third general equation of hydrodynamics, and I
have consequently not hesitated to employ the equation (a),
which is a logical consequence of that general equation, in lay-
ing a foundation for the subjoined hydrodynamical theory of the
action of a galvanic coil.
30. A current of the sether being supposed to flow uniformly
along a straight cylindrical conductor, the motion of the fluid
at any point may be determined by the following reasoning
(given in more detail in the ' Principles of Physics,' pp. 563-565) .
The motion is plainly a function of the distance from the axis of
the cylinder, but cannot be wholly parallel to it ; for if that were
the case, since the motion is, by hypothesis, steady, and in such
motion the pressure is everywhere less as the velocity is greater,
and sinc« in this instance the velocity will evidently be less the
greater the distance from the axis, it would follow that on all
sides there would be tendency to motion towards the axis, which,
if not counteracted, would put a stop to the current. To coun-.
teract this tendency there must be centrifugal force due to cir-
cular motion about the axis ; and according to the hydrodyna-
mics of steady motion the rectilinear and circular motions may
coexist. Hence, if r be the distance from the axis, and the rec-
tilinear and circular motions at that distance be respectively
F(r) and/(r), we shall have
u=^f[r), t.= -^y(r), w=¥{r).
These equations satisfy the condition of constancy of mass ex-
Phil. Mag. S. 4. Vol. 48. No. 317. Sept. 1874. O
Digitized by VjOOQ IC
194 Prof. Challis on the Hydrodynamical Theory of the
pressed by the equation
dx dy dz^ *
which is true for a compressible fluid inclusively of small terms
of the second order ; so that the subsequent reasoning, although
strictly applicable to an incompressible fluid, may be taken to
apply to the sether. Now, from the known expressions for
^« -J-} -^ for steady motions of an incompressible fluid, it
will readily be found that
W ^ {My ^ the centrifugal force.
8L These results are independent of the forms of the func-
tions f(r) and F(r) and of any relation between them. But
since the assumed values of u, v, w do not make udx + vdy + wdz
an exact differential, according to the principles maintained above,
they must be such as to satisfy the equation (a). By substitu-
ting them in that equation, and integrating, the result is
F(r) - r'
c being the arbitrary constant introduced by the integration.
We have thus demonstrated that the current must be such as to
satisfy the relation between the velocities/(r) and F(r) indicated
by this equation.
32. By taking account of this relation the equation
udx + vdy '^ wdz =0
gives
^^ " rW) ^^^^^y^ ^ ^ (xdy-ydx).
Hence, by integration,
xrssctan"*- +J,
X
which is the general equation of the surfaces of displacement,
the orthogonfd trajectories of which determine the directions of
the motion. If tan~'-a^, and r, be a given distance from the
axis, we have
which shows that the motion in the cylindrical surface of radius
r, consists of spiral motions the directions of which make with
Digitized by VjOOQ IC
Action of a Oalvcmic Coil on an external email Magnet. 196
parallels to the axis the angle whose tangent is -^. The motion
is thus completely determined if only the forms of the functions
f(r) and F(r) can be found. In my work already cited I have
expressed (in p. 566) a doubt as to the practicability of doing
this in the existing state of hydrodynamics. I have/ however,
since discovered the following argument, which I consider to be
adequate to this purpose.
33. Suppose the straight galvanic current to be cut by a plane
transversely, and on the plane three concentric circles to be de-
scribed having the common centre on the axis, and let their
rady be r+«, r, and r— «, « being verj' small. Also let there be
drawn in the plane from that centre two straight lines separated
by the small angle 80. Then the space bounded by these lines
and the first and second circles is ((r+«)*— ^))-o-# ^^^ ^^^^
bounded by the same lines and the second and third circles is
80
(r*— (r— «)*) -^. Now, according to the foregoing investigation,
these spaces may be considered to be transverse sections of ele-
mentary channels in which the galvanic current is constrained to
move. Let V be the mean velocity of the current through the
space furthest from the axis, and V that of the current through
the other. Then, inclusively of small terms of the second order,
V'=F fr+ ^Yand V=F(r- ^Y Hence the excess of fluid
which in a second of time passes through the larger space above
that which in the same time passes through the other is
which, omitting terms containing efi &c., becomes
34. We have now to take into account the principle adverted
to in art. 11, according to which the inertia of an unlimited mass
of incompressible fluid opposes an insuperable obstacle to any
alteration of the quantities of the mass on the two sides of any
unlimited fixed plane. Since in the case of the galvanic current
fluid is being transferred every instant across the above-men-
tioned transverse plane, not only roust the rheophore furnish a
channel for the circulation of the fluid, but there must also be a
general stress, like hydrostatic pressure, which, taking effect
always in the directions of any channels of circulation, maintains
02
Digitized by VjOOQ IC
196 Prof. Challis on the Hydrodynamical Theory of the
the current in opposition to the tendency of the inertia of the
fluid to put a stop to it. In the present theory this stress is due
to the action of the battery ; the wire supplies a channel for the
current; and^ as is shown in art. 11^ it is dynamically necessary
that the current should flow in a complete circuit.
35. It is clearly possible that the form of the function F(r)
might be determined by arbitrary conditions. For instance^ if
the above-mentioned stress were arbitrarily caused to be the same
at all points of the transverse plane^ the velocity parallel to the
axis would be the same at all points^ and F(r) would be a constant.
But it is evident that this is not true of a galvanic current. The
principle of the present inquiry demands that as a definite rela-
tion between the functions y][r) and F(r) was obtained in a unique
manner by integration^ the form of the function F(r) should be
similarly determined. Now the only way in which that form can
be obtained exclusively by integration is to equate to zero the
above factor — ^ H — "> > ^^ which case integration gives
Thus the velocity parallel to the axis varies inversely as the dis-
tance from the axis ; and the stress which maintains that velocity,
and is therefore proportional to it^ varies according to the same
law. Since the transverse sections of the elementary channels
above defined vary directly as the distances^ it follows that
through each elementary channel outside the wire the same
quantity of fluid flows in a given interval. Also^ since it has
c
been shown (art. 31) that/(r)= - F(r), we obtain
or the transverse circular motion varies inversely as the square
of the distance. These results are essential to the hydrodyna-
mical theory of galvanism.
36. But for the theory of the action of a galvanic coil we re-
quire to know the motion of an setherial current along a fine
wire the axis of which has the form of a circle^ and the trans-
verse section of which is circular and uniform. For this case it
will be assumed that^ by reason of symmetry^ the motion at any
given point is compounded of motion parallel to the axis^ and of
motion in the plane passing through the point and the centre of
the axis^ and cutting the axis at right angles. Let the plane of
this axis be parallel to that of xy, and its centre be on the axis
of z 'i and let h be the height above the plane xy of the point of
intersection of the circular axis by the above-mentioned trans-
Digitized by VjOOQ IC
Action of a Galvanic Coil on an external small Magnet. 197
verse plane^ and a the distance of the same point from the axis
of z. Also in the same plane let r and 0 be the polar coordi-
nates of the given point P referred to the point of intersection
as pole^ and to the straight line through the pole parallel to the
plane xy. Then, the rectangular coordinates of P being x, y, z^
if we put R for (a?'-f y')^, and suppose the velocity parallel to
the plane ocy to be F(R, z), and that in the transverse plane to
be f{r, 0), we have
together with the equalities r* = (z — A)* -f (R — a)*, and
z~-k
tan tf = p . By analytical operations, the details of which, as
being somewhat long but presenting no difficulties, are not in-
serted here, it may be shown (1) that 7" + T" + ;/~=0#
(2) that udx+vdy-hwdz is not an exact differential; (8) that by
substitution in the equation {a) there results the following equa-
tion of condition connecting the functions / and F :
37. Respecting this equation we may, first, remark that since
it does not contain ^ it shows that the assumed motion requires
that /should be a function of r only, and consequently the mo-
tion in planes transverse to the axis of the wire is proved to be
circular. This result is in accordance with the original assump-
tion, that the transverse section of the wire is circular, as should
plainly be the case, since the surface of the wire bounds the cir-
cular motion.
38. The proof that /is a function of r only having taken no
account of the magnitude of a, and being clearly independent of
that of h, we may infer that the function has the same form
whatever be the radius of the axis of the wire, and therefore the
same as if the radius were infinite, in which case a finite portion
of the wire might be considered to be a straight cylinder. But
we have shown (art. 35) that for the straight cylinder/(^r) = 4.
Consequently, substituting this value of /(r) in the equation (i),
Digitized by VjOOQ IC
198 Prof. Challis on the Hydrodynamicd Theory of the
there results for determining the form of the function F the
equation
-2+W-|J(-*)-v^(«-)=0-
This partial differential equation integrated in the usual way
gives
*'"'II(z-A)'*U-a)-
Now it is certain that the expression for the velocity F(R, z)
must involve the distance r of the point P from the axis of the
wire. This condition is satisfied by the above value of F by
assuming that
*fe-)-('-f^T'
and can be satisfied in no other way. We have therefore the
unique solution
p_ C, C^
R((^»A)«+ (R-fl)«)i ^
C, being an arbitrary constant. Thus exact expressions for the
velocity in any plane transverse to the axis and for that parallel
to the axis having been found, the total motion, which is com-
posed of these two, is completdy determined.
89. From the above expression for F, that which applies to a
straight cylindrical wire mav readily be deduced. For putting
a + « for R, ft being a variable quantity restricted within compa-
ratively small limits, and giving to C, the form {/a, </ being an
arbitrary factor, we have
F= '^'^ ""'
(fl+«)r
('-i>
which for a straight wire, for which a is infinite, becomes
r
agreeing with the result obtained in art. 35.
40. It would seem that the foregoing investigation might be
-generalized so as to apply to a wire conductor of any form, when
it is considered that the determinations in arts. 30-35 of the
forms of F(r) and/(r) for a straight cylinder did not involve the
length of the axis, and would remain the same for a cylinder of
infiinitesimal length if the condition of circular motion about the
axis were satisfied. We have shown that this condition is in fact
satisfied by a uniform conductor of circular form, which may be
regarded as made up of a series of right cylinders of infinitesimal
Digitized by VjOOQ IC
Action of a Galvanic Coil on an external small Magnet. 199
lengths ; and as any portion of a uniform conductor of any form
may be supposed to be similarly composed^ the expressions for
/(r) and F(r) for a circular wire would appear to apply generally^
if the radius a be taken to represent the varying radius of curva-
ture of the axis of the wire. This question^ however^ requires
more consideration than I can now give to it.
41. Returning now to the circular conductor^ if in the expres-
sions for u, V, w in art. 36 the values found for /(r, 6) and
F(R, z) be substituted, we shall have
cjp{z-h) c^
c^yjz'-h) _ c^
^^ R/^ RV
g|(R-"a)
Hence, since R*=^+y* and r*= (ar— A)«+ (R_fl)«, it will be
found that
^ r (z— A)*4-(R— «)* r x^ + y^
Consequently the right-hand side of this equation becomes an
exact differential when multiplied by the factor r. Before pro-
ceeding to the next step, it is necessary to take into account that
in the foregoing investigation the arbitrary constants e, and c^
have been introduced in such manner as to show that they
are wholly independent of each other. Hence, on equating
r{udx+vdy+wdz) to zero, we must have separately
(z— A)dR — (R--g)ig _^ ydx—xdy __^
which means that both the motion transverse to the axis of the
wire and that parallel to the same are such as require a factor
for making udx + vdy + wdz integrable. Both are steady motions
and therefore coexist. Instead of the above two equations we
may, by introducing an arbitrary constant factor X, employ the
single equation
(z— A)rfR- (R,—a)dz ydx—xdy __^
Hence, by integration,
C=c,tan-*^^^+\Cjtan-*^ssCi^H-\c^,
supposing that ^=tan^, and, as before, that =-— = tantf.
Digitized by VjOOQ IC
200 Prof. A. Stoletow on the Magnetization- Functions
DiffereDtiating this last equation^ we get 0=c d0+\c^<f>, or
dif}'^ c,
42. Assuming that c^ and c, are positive quantities in the
expressions for u, v, w in art. 41, it will be seen that those values
were formed so that 6 and <b each decrease with the motion.
Hence ^will be positive, and X must be a negative quan-
tity. According to the supposed directions of the decrements,
the spiral motion will be dextrorsum. If the motion were
assumed to be such that d0 and d<f> had different signs, the
spiral motion would be sinistrorsum, and we might by the same
reasoning as before obtain C=c^6'\'\^c^<f>, c^ and c^ being still
positive. In that case tt = ^= a negative quantity, and V
is consequently positive. As the factors X and X' are wholly
arbitrary, we have thus shown that, as far as hydrodynamics is
concerned, the galvanic current might be either dexirorsum or
sinistrorsum.
Having in the preliminary part of this communication dis-
cussed the action of a large magnet on a small one, and having
now ascertained the exact form of a galvanic current along a cir-
cular wire, I propose in a second Part to investigate the action
of a galvanic coil on a small magnet, and to show why it agrees
approximately with that of a magnet, and in what respect espe-
cially the two actions differ. In the course of the investigation
the facts on which Ampere's theory rests will be accounted for
by the hydrodynamical theory, for the purpose of fully establish-
ing the claim of the latter to be considered a strictly h priori
theory.
Cambridge, August 10, 1874.
XXX. On the Magnetization-Functions of various Iron Bodies,
By Professor A. Stoletow*.
IN my work on the magnetization of ironf I have taken
Neumann's coefiScient « as a measure of the magnetizability.
This, as is well known, expresses the ratio in which the magnetic
moment, referred to the unit of volume, stands to the quantity
of the magnetizing force, presupposing that the iron forms an
* Translated, from a separate impression communicated by the Author,
from the Bulletin de la SocUt4 Imp, des Naturalistes de Moscou, 1873,
No. 4.
t Pogg. Ann. vol. cxliv. p. 439; Phil. Mag. S. 4. vol. xlv. p. 40 ; more
fully at a separate brochure in Russian, Moscow, 1872.
Digitized by VjOOQ IC
of various Iron Bodies. 20 1
nfiaitely long cylinder and is uniformly magnetized longitadi-
nally. I have named this coefficient (in that essay denoted by
k) the magnetizing -function of the given iron, since it depends
on the quantity of the magnetizing force. A.n analysis, namely^
of the experiments of Quintus Icilius (with ellipsoids) and of
my own (with a ring) showed that the function k at first in-
creases rapidly as the decomposing force rises^ and then again
diminishes. This behavour seems to take place with all sorts of
iron ; yet the absolute numerical values of ky with the same val ue
of the argument, are very different, according to the quality of
the iron. These results have been corroborated by a thoroug h
investigation by Mr. H. A. Rowland*. He shows that the
course of the function k is precisely similar for steel and nic kel
as well as iron, and can be represented by the same empiric
formula, but that the constants of the formula, even for two
varieties of one and the same metal, come out very different f*
Professor Biecke, in his '' Contributions to the Knowledge of
the Magnetization of Soft Iron '' (Pogg. Ann, vol. cxlix. p. 433),
proposes, instead of the magnetizing-function of the infinite
cylinder, to consider another function p, which has the same
signification in reference to the sphere.
The two quantities, referred to the same decomposing force,
* '* On Magnetic Permeability, and the Maximum of Magnetism of Iron,
Steel, and Nickel," Phil. Mag. August 1873, p. 140. The term "mag-
netic permeability " is used, alter Sir W. Thomson, to denote the quantity
/t=l4-4iriir, which, as ib is here generally much greater than unity, varies
nearly proportionally with k,
t Professor Wiedemann, when discussing my work (in Galvanismus^
2nd ed. vol. ii. p. 518), regards the function which is calculated from ex-
periments with the ring as another magnetization-function, not to be con-
founded with that obtained from experiments with *' unclosed systems."
There does not seem to me sufficient reason for this distinction. Residual
magnetism, which is here in question, is present in burs also. If we con-
sider a veiy thin and lon^ bar and a ring, both magnetized uniformly, the
difference between them m relation to the residual magnetism is hardly to
be reckoned considerable. The demagnetizing force proceeding from the
mass of its iron wiU in the ring be equal to nil; in the bar it is a small
CO
quantity, of the order of ~p, where a> is the cross section, and / the length
of the bar. (Maxwell, ' Treatise on Electricity and Magnetism,' vol. ii.
p. 67.) In both cases an external force is requisite in order to expel the
residual magnetism. If we always observe the reversal of the magnetism
of the iron, the calculation of k is only to this extent vitiated by the residual
magnetism, that a certain portion of the reversed decomposing force is ex-
E ended in discharging it. But M. Wiedemann's own experiments with
ars, and those of Poggendorff with closed systems (Wiedemann, /. c.p.519),
show that that portion is only very little.
A survey of the numbers obtained by Mr. Rowland, partly with bars,
partly with rings, establishes that the most essential cause of^^ their differ-
ence is not the form, but the quality of the material.
Digitized by VjOOQ IC
202 Prof. A. Stoletow on the Magnetxzation^Fimctumi
are connected by the relation
P-
49r 1
3 ■*■*
The function py he says, deserves the preference because^
" within a very large sphere of magnetizing forces^ it possesses
a nearly constant value for all sorts of iron '^ (/. c. p. 435). The
values of j9 calculated by M. Riecke from his own and others'
experiments do in fact accord very well; they give (p. 470) as
mean value for moderate decomposing forces the number 0*2372^
and as maximum value
;>=0-2382.
The purpose of the present note is to bring out that these
results are self-evident, and the above numbers have a very
simple meaning ; they are, namely, pretty close approximations
to the number
^ =0-2387,
47r
which is obtained as the upper limit of p when we put A:= oo,
and consequently represents the ideal maximum of p. With
moderate decomposing forces t is always small compMfed with —
(since A here lies somewhere between 20 and 200*), and may, in
the first approximation, be neglected. On this account p remains
always nearly constant and independent of the quality of the iron\.
Indeed, for every other strongly magnetic material, about the
same value of j9 would result ;(.
From this we see, on the one hand, that the numbers calcu-
lated by M. Riecke furnish a fair confirmation of the theoretical
consideration ; but, at the same time, we see that the quantity p
is very little suitable for characterizing the magnetizability of a
material, since for the sphere the influence of the quality of the
substance nearly vanishes before the influence of the form. It
can be proved that this holds good generally for every body the
* For my iron ringthe maximum of k wat => 174 ; with the kinds of iron
investigated by Mr. Rowland it was in nearly every case higher, and in one
case reached the value Ar=4d9 {fk^bSXb).
t A brief note in reference to this I find in Wiedemann's Gahamtmrns^
2nd ed. vol. ii. p. 403.
X For a ring of annealed nickel Mr. Rowland found the maximum of
its 24 (/iss305). According to this, even for nickel (at its maximum of
inagnetizability) p may reach the value 0*2364. For sted the approxima-
tion to the absolute maximum 0*2387 becomes still closer, and holds be-
tween wider Umits of the decomposing force.
Digitized by VjOOQ IC
of various Iron Bodies. 203
dimensions of which in all directions are of the same order*. In
order to calculate it priori, with satisfactory accuracy, the mag-
netization of bodies so formed, a rough estimation of the coeffi-
cient k is sufficient. The magnetization- functions of such bodies,
ascertained by experiments, will always exhibit much less varia-
bility than that of a thin bar or ring, of a thin plate or scale,
and may almost be regarded as constant. But if, starting from
such mean value, we try to calculate the magnetization of any
body of the category last mentioned, we may arrive at very in-
accurate results ; for, with bodies one or two dimensions 0/ which
are very small in comparison with the third, the tangential compo-
nent of the magnetic moment will, with the same decomposing
force, increase proportionally with kf. The influence of the
specific qualities of the substance appears here, therefore, in full
intensity. If we wish to bring such bodies also within the range
of our considerations, we must take into account the specific
quality of the substance, and the knowledge of the magnetiza-
tion-functions of bodies of this sort will be indispensable. The
function k perfectly suffices for this purpose, and has the advan-
tage that in it abstraction is made of the transverse dimensions
of the thin body.
Those bodies the dimensions of which are of different orders
of magnitude play a peculiar part in several branches of physics.
In hydrostatics their theory is most essentially conditioned by
the capillary forces. In the science of elasticity they require a
special method of treatment ; in that of paramagnetic magneti-
zation they make a very precise knowledge of the magnetization-
functions absolutely indispensable.
Christmai (O. S.) 1873.
* Compare pp. 66-67, vol. ii. of Maxwell's Treatise — for example,
" When ic 18 a large positive quantity, the magnetization depends princi-
pally on the form of the body, and is almost mdependent of the precise
value of «c, except in the case of a longitudinal force acting on an ovoid so
donated," &c. (p. 66), We always presuppose here that the magnetiza-
tion IS uniform.
Jc
t More strictly, proportionally with TTTZt where c is a number vanish-
ing with the transverse dimensions, and the value of ^ is not referred to the
T
whole tangential force of decomposition T, but to TXT'* For a limited
bar €=0. These considerations explain, for example, the experiments of
Von Waltenhofen on the magnetization of bundles of thin wires, thin-
walled tubes, &c. (Wiedemann's Galvanismus, 2nd ed. vol. ii. p. 430). The
great power of the magnets composed of thin bands of steel (rubans d'acier)
of M. Jamin ( Comptes Rendus, vol. Ixxvi. p. 789) appears also to stand in
relation therewith (compare especially art. X. p. 794).
Digitized by VjOOQ IC
[ 204 ]
XXXI. On Tides and Waves,— Deflection Theory.
By Alfred Tyloe, F,G.S.
[With Three Plates.]
To the Editors of the Philosophical Magazine and Journal.
Gentlemen^ London, August 15th, 1874.
I SHOULD be glad if any of your readers will send me a re-
ference to any work of authority in which there is any direct
statement of the height of the level of the ocean (say the central
Atlantic) compared with high-water mark on the east and west
coasts of Ireland and England. This is an important point in
the general theory of the tides^ a subject I am about to dis-
cuss. The view I shall advocate is that the level of the ocean is
nearly represented by high -water mark on coasts and bays where
there is free access of the tide and a channel without a sudden
taper. Mr. E. Roberts^ of the Nautical Almanac OfiSce, editor
of the Reports of the Tidal Committee of the British Associa-
tion^ informed me last month he was not aware of any statement
in print on good authority on this point. The only opinion I
have on this subject is from Professor 6. G. Stokes^ F.R.S. (and
that is an unprinted one*), who wrote, " Nobody maintains that
the general level of the ocean is that of low water ; it is the
mean between high and low, except in shallow channels &;c.,
where it is not the exact mean/^ In the absence of further
authorities I shall give my deflection theory of tides.
In Plates II. and III. I give a drawing of what I suppose is the
relation of high and low water on the coast and in estuaries and
channels to that of the sea. I show that the level of the central
ocean approximates to mean high-water mark on the coast of
Ireland, and is about 4 feet above the English Ordnance Datum,
which datum may be treated as an arbitrary line, being only the
mean level of the sea at Liverpool, Penzance, and Falmouth, all
places in which the tide is affected by the converging contour
of the coast.
The velocity of the central ocean- stream, if reduced by the
inequalities of the sea-bottom at a different ratio to the depth,
would cause the water to heap, and vice versd. I do not think
it does heap perceptibly until near the coast, and then in very
different degrees (see Plates II. and III.). When the increase
of velocity exactly balances the decrease of depth ; that is, using
Y and v for the old and new velocity, and I and t for the re-
spective distances from the centre of the earth,
V n
when I = t, then — = ^ (1)
* In some remarks about the views expressed in Plates IL and IIL sent
to him for examination, March 7; 1874.
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f 1
Median/
-"•^^'SS^-
22[flia5&:
*W^^
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Mr. A. Tylor on Tides and Waves. 205
This is the equatioo to equilibrium of the ocean-surface in the
case where no interfering currents, caused by difference of tern-
perature in the ocean, are present*. A complete oceanic tide
stretches from coast to coast, and is always divided into three
regions (central, anterior flowing, and posterior ebbing), re-
versing direction each six hours ; that is, in the part where there
was propulsion, aspiration succeeds, and vice versd. A perfect
tide would stretch over a space on parallel of latitude repre-
sented by the rotation of the earth in six hours.
The mass of tbe central ocean is represented, in PI. 11. figs.
1 and 2, and PI. III. fig. 1, as moving 180 feet per hour on
the average of each tide of six hours, but in alternate and oppo-
site directions. A movement of 3 feet per minute in the cen-
tral ocean 20,000 feet deep would communicate a velocity of
three miles an hour where the water was 238 feet deep, by the
composition of forces. 1 suppose that this slow motion in a
vast mass of water of great and equal depth would be horizontal
alone, as it is not possible to suppose vertical motion without
creating a gap below or behind the tidal current. The hori-
zontal motion would be also limited ; for the sum of the motion
of all the particles of water in the Atlantic tidal stream could
not exceed the area of the gap emptied and filled on the oppo-
site coasts of the Atlantic each alternate tide. In this respect
the tide is like a wave, the relation of whose movements to
the size of the gap made when generated is clearly shown in
fig. 1 (p. 216). The force of the moon will be estimated; and
the relation of its attraction to a particle on the ocean is shown
in fig. 4, PL IV. The direction in which the moon can affect
* From the equation Q=AV, using Q and g for discharge per second,
and A for cross section, and from observation, I have
i - vTi • ■ <^>- "- '^'^¥1 " V -^/iA ■ • • <^>
from which I obtain a new equation to the flow of water in uniform motion
— that is, only when V=r. This is
i=KM) <^'
which applies to water in canals in uniform motion, as in fi^. 3, Plate III.
The tendency of every river is to approximate in all parts of its course to a
uniform mean velocity. The river carries sand and mud from the mountuios
to the sea along its channel at a nearly uniform rate. Increase of quantity
of water flowing at any point balances decrease of slope throughout all
livers. A steamer ascending the Rhine meets a current descending at one
velocity at different slopes. This is proved by the consumption of fuel
being equal per mile from the sea to Mayence, except where back-water
on one side increases velocity on the other, or where shallows retard the
ship. I do not find (R the mean hydrauUc depth) of value in calculations.
Digitized by VjOOQ IC
206 Mr. A. Tylor on Tides and Wavu.
particles of water and move them is represented in a new manner.
The sun's effect can be calculated similarly to the moon^s.
The attraction of the moon when in a vertical line would not
produce any horizontal or vertical movement in a particle of
water below it ; and the attraction could not produce a heap of
water below it without the water being propelled from some
point of the ocean on which the rays of attraction fell at an angle
less than 90° ; and then I do not think the heap could exceed
2 inches in height*, for reasons which will be given hereafter.
The mass of the moon is equal to a spherci^of 118*75 miles
diameter of the same density as the earthy and situated at 3956
miles from the point to be attracted — that is^ at the distance
of the radius of the earth. The circle F near C (fig. 4, PI. IV.)
should be only one sixth of an inch if drawn to scale. It'
is shown in the position in which it would i«present the action
of the moon on the ocean if it revolved round C in a lunar
month. Thus any point on the circumference of the earth must
be attracted to the centre of the earth by an attraction greater
than that of the moon to the same point in the ratio of 295520
to ]. For 60*263«=8681, and 60263 is the mean distance
of the moon from the earth ; then the density of the earth is to
that of the moon as 1*647 to 1^ and the mass of the earth to
that of the moon as 49*5 to 1. Then
3631 X 49-5 X 1647=295520;
that is, the effect of the attraction of the moon in a particle on
the surface of the earth (at the moon^s mean distance) is only
^—^ of that arising from the attraction of the earth itself f.
The weight of any body on the earth would therefore be
lightened in that ratio, or in the proportion of 1 grain to 4^
gallons of water (70^000 grains to the gallon), the moon being
* This is a different case altogether from that of tbe estimate of coUec-
tion of water at the equator; and the practical test given above is better
than'theoiy.
t This IS calculated differently in a note to page 628, Herschers * Out-
lines of Astronomy/ 1873 : the cube of the sun's distance is erroneously in-
troduced into the calculation for finding the moon's maximum power to
disturb the water in the surface of the earth ; this brings the relative effect
of the moon's attraction to-jyr^VTinr of K^s^vity, according to Herschel.
This, however, is only -^^ ot the real quantity. My calculation is ac-
cording to the following law:— "Two such globes would (by the same
proposition) attract one another with a force decreasing in the duplicate
proportion of the distance between their centres " (Newton, page 24, edit.
819). If Herschel's figures were correct, we should have tides of 3 inches
on our coast instead of 12 feet in height. Also the fictitious moon F placed
near C (fig. 4, PI. IV.^, to represent the effect of the real moon, would
have only a diameter of 34*03 miles, and contain 2^,629 cubic miles instead
of the larger quantity mentioned by me in tbe text. ,
?;
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Ph2lMag.&4.Vol48.Pl.m.
MMIIs ~
tsgirw oyer ^tetBar-withMV Iflsavpttydj^^
ter mde^,runmjy at^wMmey^^fetd^oiin.
u , „ • supposed^ tahe ^tatUmary .
NOTE For oalcuJUUxnf rAoeuty c^Wbitr w
itrdi/fbwUmjKUrMtdi^ArMeCa^
Thus, v^ fO ^.i mr y " 36 J^.v . or/uf&
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Mr. A. Tylor on Tides and Waves. 207
at its mean distance. The attraction of the moon I calculate to
be one fifteenth greater at a point on the near side of the earth
than at a point vertically below it on the offside at the antipodes.
Every day the change of position of the moon with regard to
the earth would affect all weights on the surface of the earth
temporarily^ but only to the extent of 1 grain in 61 gallons^ a
quantity which is not susceptible of measurement by a balance.
The effect of the moon^s direct attraction is really very small
on each cubic foot; but as it affects water at the bottom of
the sea nearly as much as on the surface^ it amounts to an
enormous moving force when a stream 20^000 feet deep is set
in motion. It is only perceptible to observation when motion
is accumulated by composition at certain points^ such as where
there is a great composition of forces^ as in soundings. Navi-
gators do not observe the motion of the tide except near the
coast. I calculate the amount in the following manner. If
the effective force of 'the moon has to be multiplied eighty-four
times to raise a 12-foot tide at a point of the coast where the
sea is 238 feet deep^ then the direct effect of the moon's attrac-
tion on water 238 feet deep would only be \ foot^ or something
under 2 inches. Thus T consider 2 inches is the greatest height
that the moon could possibly raise the level of the sea under it
with 238 feet depth of water^ |~J- of the elevation of 12 feet
being the effect produced in deeper water by the moon and
sun, transferred by the composition of forces to shallow water.
The drawings (figs. 1, 2, and 3, PI. IV.) from standard works
on tides are therefore great exaggerations by their authors ; and
the descriptions accompanying them would lead any one to
suppose a great heap of water could be rapidly accumulated in
the central ocean by vertical attraction on deep water. The
authors do not specify how the water is obtained, or whence it is
comes, or the data by which they prove such a heaping up
possible as is proposed by the equilibrium theory.
Time is the essence of such an operation, which, if done at
all, must be completed in six hours, or a contrary current would
set in. The heaping-up movement, to keep up with the rota-
tion of the earth, would have, in the latitude of Brest, to make
water flow at 11*3 miles per minute, which is clearly impossible.
It is not, therefore, surprising that the effect of the tidal wave is
hardly perceptible at oceanic islands, whereas, if figs. 1, 2, and 3,
PI. IV., were correct, it ought to be as large there as on the
mainland coast.
Fig. 1, PI. IV. is an explanation of the tides copied from the
' Penny Cyclopsedia ; ' figs. 2 and 3, PI. IV., are from Dr. Lard-
ner's ' Astronomy,' pp. 324-5 ; and my own view is given in
fig. 4; so that the reader may compare the different theories.
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208 Mr. A. Tylor on Tides and Waves.
If fig. 4, PI. IV., is correct, there can be no great heaping up
of water or any tidal wave generated in one direction, as has
been sometimes assumed ; for I show that the action of the tide
is a reciprocating action, and has as much motion from west to
east as from east to west.
The assumption of a great heap of water travelling in one
direction, or producing a certain amount of retardation of
the rotary movement of the earth, quite unbalanced by ac-
celeration, has been taken as a serious fact; many writers
of reputation have supposed that the rotation of the earth
must be affected by this hypothetical wave-action in one di-
rection.
My view of the general theory of the tides (fig. 4, PI. IV.)
differs materially from those generally accepted ; and I cannot
understand the existence of an intumescence (shown in figs. 1,
2, and 3, PI. IV.) under the moon at all if the subject is treated
in the ordinary manner of reasoning.
I entirely disbelieve in tidal action having the smallest effect
on the rotation of the earth. It is a balanced action. The sun
might produce currents by unequally heating water, which
might affect the surface-level of the sea and cause inequalities ;
but of this there is no positive evidence. I show by fig. 3, PI. III.
that, under certain circumstances observed, a curi'ent may travel
against the slope of the surface. This I noticed in your Journal
in 1853. The existence of a current is of itself, therefore, no
proof of what is the direction of the slope of the surface. I find
that an elevation of level of 2 inches on the east maintained over
the west side of the Atlantic, or ince versd, where water is very
deep, would generate a current of 3 feet per minute in the ocean
in the direction of the slope, supposing the Gulf-stream did
not intervene and there was no tidal action. The western water
would take 5 years to cross the Atlantic at a speed of 3 feet
per minute, to reestablish equilibrium. If the difference of level
were produced by luni-solar action, it would cause no current
until the force creating it was withdrawn.
If 58 miles per hour is the greatest velocity a surface- wave
could travel at in the deepest part of the Atlantic, such an in-
tumescence, even if maintained, would have only proceeded 348
miles before the moon's influence would be exerted against its
motion. The great earthquake-impulse of Lisbon in 1755, pro-
ceeding through deep water, did not travel to Barbadoes faster
than 6 niiles per minute; and an intumescence of equal force or
impulse created on the W. coast of America, in the latitude of
Brest, would meet contrary luni-solar attractions when half-
way across the Atlantic. No intumescence could be raised in
deep water without forming a gap below.
Digitized by VjOOQ IC
*teOT/
Phil.Mag.S.4Afol.48.H.IV.
Qiope, is fapponed to i«r?oWe in the circle A.E.B. W in 24 >
fhe sMne niean yeloeity each 24 hoan,)»is retarded and
at the exact lunar hours marked, but within them
VerticaL
>od tide.
loean below the speed of the earth-baain holding it,
_iiP9Fy:Aot the rotation) at ebb tide shown in B. B. and W. A,,
Jl/. J/, isesca flowing ti de as in A. B. and B. W. Fig. 4 plate IV.
^
ition in alternate directions, the real mean velocity
the one direction, and only difference of speed is
>oking from one to the other only can estimate the
it of America, for there the ebb tide is in tbe direction
oceanic water and a flowing tide before it (propulsion ) .
I
I present, Jointly attracted by Mi.Mii, attraction
'/?tnC/^e time. The resultant motion of the particle P n. is
Jf,JlT, article P. IV is in a contrary direction, because th«
^through the Earth, deflected by meeting the curved
Lhich accelerates the ocean in the direction of B to W.
Aon of £ to B, and the force M. iv being deflected
on to P. vm and retards water in tbe quadrant W A.
Itw."
kuses alack tide at low and high water.
>f the Barth deflecting attraction rays at vari(>us
near C, Pig. 4, plate iv supposed when revolving
M^ do.
»een accelerated above US per minute back to that
)w water for convenience. 1 omit the action of
ience.
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Mr. A. Tylor on Tides and Waves. 209
In fig. 4, PI. IV.^ I take a particle of water at certain points on
opposite hemispheres^ and show the direction of the resultants
of the two forces (the moon and earth's attraction) and the pro-
bable deflection of the moon's attractive rays in passing through
the earth. Sir J. Herschel (p. 528) only gives one position on
his Plate (p. 464), and leaves it to the reader to try the position
of particles on other parts of the circle and find their direction.
I have tried to do so according to his rule, and find that his
diagram would only apply to the moon's attraction by the earth
at such an immense distance that gravity could be considered as
acting to and from single points, viz. the centres of the two
attracting bodies, and surface attractions need not be considered.
Now the case of the tides is clearly that of a point or particle
at the surface of the earth being attracted by the two centres of
the earth and moon. IlerschePs figure (p. 464) is not appropri-
ate to the conditions of the tides ; iot it has no special relation
to surface attraction at all. If it proved any thing about tides,
it would prove there would only be a tide every twenty-four
hours. On the contrary, in fig. 4, PI. IV., I take into account
the deflection of the rays of attraction on entering the earth,
and find that, if they pass through the earth with the rapidity
of light, when they reach the other hemisphere they cause a
twelve-hours tide, simultaneously produced to that on the oppo-
site side of the globe.
I have proved by analyzing the experin^euts on waves
by J. S. Russell and by Darcy, that the velocity measured in
feet per second of any wave when generated does not exceed
three times the cube root oi' the depth of the water it was gene-
rated in, measured in feet; that is, v=B\/p, a new formula,
which answers both for small and great depths, the usual for-
mulae giving results much too high for waves generated in deep
water.
. Mr. W. Parkes (Phil. Trans. 1868) suggests that the al-
4emate tides are produced in different hemispheres, and that
the evening tide which reaches Kurrachee twelve hours after
the morning has travelled a greater distance. This does not
seem probable; nor does he give any evidence on the point.
Then, with regard to the diurnal variations of the two tides,
Mr. W. Parkes (p. 686y says the diurnal inequalities disappear
when the attracting bodies are in the plane of the equator. It
appears to me, from the observations at Kurrachee, that when
the diurnal irregularity of the high-water points is at its
maximum, the diurnal irregularity of the low-water points is
at its minimum, and vice versd. Curiously enough, at Kurra-
chee the mean diurnal low-water irregularity is about 2 feet,
against about 1 foot (the mean diurnal irregularity of the high
P/iiL Mag. S. 4. Vol. 48. No. 317. Sept. 1874. P
Digitized by VjOOQ IC
310 Mr. A. Tylor en Tides and Waves.
water). Tbat is, instead of tV of the height of this lunar portion
of the tide representing the diurnal irregularity (which I con-
sider is the mean of the world), at Kurrachee the tides are so
exceptional that the diurnal irregularity amounts at low water to
if and at high water to | of the total height on the average of
the tides for a month, lliis opposite action cannot be owing
to the position of the attracting bodies in the respective tides
being in the plane of the equator.
I would observe that the deep central ocean without any
vertical tidal movement or tide-wave observed is certainly forty
times as large as the shallow coast^sea, where a rise of tide is
observable. The composers of figs. 1, 2, and 3, PI. 1V.| seem
to r^ard the coast alone, which I consider the exception.
They do not seem to think of the tidal conditions in the great
mass of the ocean at all in forming their theory*
It appears from figs. 1 and 2, PI. II., and fig. 1, PL III.,
from observation, that the level of the sea at high water, even
in the tidal estuary of the lliames, is only raised 5 feet, and in
that of the Clyde 1 foot, above the central ocean.
The high-water points from Falmouth to Sheemess are nearly
level; they only deviate 1 foot in 500 miles from a straight line.
The fact has not been sufficiently considered, that water in
open channels can be moved under certain conditions against
gravity, and that the great central mass of the ocean swinging
backiN^irds and forwards every six hours is one of the forces that
can easily overeome gravity when producing a slow current. As
early as 1868 I gave a drawing in your Journal (p. 259) of the
bottom-water outside the bar of the Mississippi being raised to
the surface 16 feet against gravity by the current of fresh water
flowing outwards, partly impelled by gravity (propulsion) and
partly sucked or drawn by the tidal water in front of it (aspira-
tion) : see fig. 4, PL III. I still believe that the tidal current
acts like the piston of a pump, and reduees the pressure in its
rear, and draws or sucks out the coast-water after it in the ebb-
tide, and piQshes the water back again to fill up the gap when
its notion is reversed by the luni-solar force in the flowing tide.
I first observed evidence of this action on the bars of rivers, and
represent it in fig. 2, PI. III. As the water in the Mississippi
is 100 feet deep at a comparatively short distance behind the
bar BC, and is in motion from^ top to bottom, the lower
water is evidently drawn over the bar and up an asceut of 84
feet against gravity, by the pressure of the water at B C on
the bar being reduced by the tide or mass of oceanic water mo-
ving steadily before it. Motion, of course, ensues in the direc-
* Humpbrys and Abbott record rapid motion at the bottom at Carrol-
iqn, page 149.
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Mr. A. Tylor on Tides and Waves. 211
tion of least pressure ; and that happens to be^ as far as the upper
part of the water is ooneerned, against gravity, and is similar to
what happens in a mill-raee (fig. 8, PI. III.). This action,
which takes place at the mouths of all large rivers, is a clue to
the tidal movements. It is true that in the Severn at Beachley
the high-water level of spring tides is 25 feet above the
Ordnance Datum, and 21 feet above the level of the central
ocean. But this is an exceptional case that can be explained.
At Beachley at high water the cross section is 400,000 sup. feet,
and at low water only 25,000 sup. feet (see fig. 1, PI. II.)-
At Stonebench, 36 miles higher, there is only a cross section
of 240 feet, and a depth of 8 feet at low water.
The cross section at Beachley is not a tenth of the sexstion a
few miles lower down in the Bristol Channel.
The exceptional height of the tide there is solely due to the
funnel shape of the c^nnel, caused by the hard recks that pre-
vent the tideway being excavated to the usual form. This
exception proves the rule. I compare the ebb-tide to the action
of a mill-stream, thus i-^
Fig 8, PL III., represents, from actual observation, a case
of water moving against gravity in an open channel, and against
the direction of the slope of the surface of the water. The
atream of water passing over the weir at B falls in a thin stream at
great velocity to C^. Here it changes its direction and the current
is against the slope of the surface, vis. towards D^ instead of
towards C^, which would be the direction of gravity. The
stream D E in uniform motion niduces the pressure at D and
draws the water from C after it— just as the great central
oceanic stream represented in figs. 1 and 2,. PI. II., and in
fig. 1, Plate III., draws the coast-water westwards and forms a
gap which is filled by the tide, the oceanic stream having reversed
its direction in six hours, as shown in fi^« % PL IV., by luni-
solar attraction pushing on to the coast-hne the flowing tide.
My explanation of Che luni-solar attraction in fig. 4, PL IV.,
is placed, adjoining the drawing.
It will be observed I omit in the diagram (fig. 4, PL IV.) the eits*
tomary theoretical intumescences opposite to each other movine
with the moon, but through eadi of which every part of the earth
is supposed to pass daily, as in figs. 2 and 8, PL IV«, and I show
an alternating tide in the ocean itself instead, in fiig. 4. I con-
fess I cannot follow the supposed changes of form of the ocean-
surface in figs. 1, 2, and 8, PL IV., nor imagine either that such
movements could possibly occur, or that they .would at all de-
ncribe the tidal changes at any point of the globe as known to
obs^rvera. I remark, the writera give no dimensions of the in-
tumescences, or calculate the force to convert the circle ab into
P2
Digitized by VjOOQ IC
212 Mr. A. Tylor on Tides and Waves.
the ellipsoid a, by M. Arago very justlv wrote that '^ details are
the touchstones of theories ;'' and all details are absent in the
well-known articles on this subject. In fig. 1 the earth is
represented as a circle^ and the ocean as an ellipsoid* In figs.
2 and 3 the water is the circle^ and the earth the ellipsoid.
According to figs. 1, 2, and 8, PI. IV., the velocity of the
tide would be equal at high, low, and half tide to any observer
on the earth.
The greatest action, on the contrary, is shown to be at the half
tide, both ebb and flowing, in my diagram, fig. 4, PI. IV. Cap-
tain Beechey* remarked that the velocity of the current was
greatest at half tide ; and this disproves any theory in which
the tide is supposed theoretically equally strong at all parts.
Dr. Lardnerf explained his diagrams, figs. 2 and 3, PI. IV.,
by stating that the moon forces down the water at the sides at
right angles^o her direction, and raises it at the two ends of its
diameter pointing to her. In figs. 2 and 3, PI. IV., the moon
pulls the water in one hemisphere and pushes it away in the
other. This is the first time that the property of repulsion or
forcing has been attributed in this manner to the heavenly bodies.
He shows an exactly opposite direction of forces on the near and
far side of the earth prodbced at the same moment by the moon.
Notwithstanding any language that may be used to make
figs. 1, 2, and 8, PI. IV., appear to satisfy the actual tidal con-
ditions, it will, I think, be evident to the reader that the posi^
tions of the forces as drawn are not in accordance with the ordi-
nary laws of mechanics. Herschel refers the reader to his
drawing (Astronomy, p. 461), in which the retardation and acce^
leration of the moon in its elliptic orbit round the earth at a
mean distance sixty times the radius of the earth is proved to be
according to the law of equal spaces being described by the moon
in equal times, and consequent variation of motion.
The reader is recommended by Herschel to prove the accele-
ration or retardation of the tides from the diagram (p. 464),
which is really impossible, as the figure relates to an entirely
different case, and is in a part of his book relating to the motions
of the moon. It is admitted that the moon is a free body attracted
at a great distance by the earth, and made to mo\ e at varying velo-
cities round the earth in a lunar month at a rate dependent, among
other causes, upon the relative weights and distances of the moon
and earth, and the original impetus and angle at which these
bodies were projected into space. The tidal water, on the con-
trary, is held as- an inseparable mass of fluid reposing in a basin
of earth ; and it travels at the same uniform speed of rotation as
♦ Phil. Trans. 1851, p. 711.
t Lardner*8 'Astronomy,' p. 336.
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Mr. A. Tylor on Tides and Waves. 213
the earthy except when modified in velocity to a very small ex-
tent by the attraction of the celestial bodies, producing the tides.
The two cases are not parallel, and the diagram mentioned by
Herschel is certainly not applicable to the tides at all. The
oceanic water has no tangential force independent of the earth ;
for two points in the ocean^ reaching 180°, opposite to each other
are at the same distance from the centre of the earth, and are in
exact equilibrium if the difference of tidal action i& left out of
consideration. I think the authors have not taken into consi-
deration the fact that the rays of attraction from the moon to
the water, when the water is screened from the moon by the
earth, would pass through the earth, in order to reach the oppo-
site side, not in a straight line. They would not only lose force of
course as the square of the distance increased, but I think no
ray or vibration or impulse or line of attractive force could fall
upon or pass through a curved body such as the earth at an acute
angle without being in some way defiected or diverted from its
direct course in passing through the earth to water on the other
side ; and the reverse is true. I believe a vibration of any kind, or
attraction-ray, would have to be modified in its direction or bent
at the point of contact, so as to enter the surface of the earth at a
right angle to a[tangent of the curve at the point, as shown in fig. 4.
My own view (PI. IV. fig. 4) shows slack water at the turn
pf the tide both near high and near low water; but of course these
events do not always coincide. When the luni- solar attraction-rays
fall near A and B (fig. 4, PI. IV.), they are evidently deranged and
deflected so as to produce very little effect ; in fact the state of
the tide near those points is what might be called bordering on
motion, which state accords with observation. Although the angle
M|P^R^ is onljr i"'07y or two thirds of the angle M^^P^^R^,, yet the
factual effect m producing tidal motion is much less than that
proportion. For at P the tidal motion is being reversed^ and
the speed of the flowing tide has to be created from slack water;
while at P^^ the effect of attraction from M^^ is to accelerate the
tide then moving freely and in the same direction as it has been
between P^ and P^^ and also in the line of the earth's rotation.
The actual effect in velocity theoretically is quite four times as
much in the half hour near P^, as at that near P^ ; and this accords
with observation. The angle of the resultant B^ is found thus.
The angle M^P.C is 88^ 30? 4"=318604 seconds.
The force M.P, is to C P, as 1 to 295,520 ; .'. the angle
M|P^Bp the resultant, equals q," q^=F'07. In the same
manner the angle M^^P^,B^^=1"*66. The depth of the Atlantic
(five miles) favours movement very much, as there is room for the
force in the direction A B^ to be transferred easily into the direc-
Digitized by VjOOQ IC
214 Mr. A. Tylor on Tides and Waves.
tion P^, E, which is that of the line of rotation. In an inland sea
like the Mediterranean, where the deep water is 6000 feet, the
movement of the tide on the coast is often not more than 1 foot.
There are 7-feet tides in one or two places in the Mediterranean
where the contour of the coast is like onr Bristol ChanneL
If the deep water in the Mediterranean Sea were one twelfth
of the depth of that in the Atlantic, we should expect a 1-foot tide
there in place of a 12-feet, according to the law of compositimi
of forces'!'. The peculiar circumstances of the Mediterranean
make the tides much smaller than I should have calculated from
the experience of the Atlantic. Taking 6000 feet as the basis of
the deep water and 9 inches as the tide, diffusion of the tidal force
from deep central to surrounding shallow coast-basins seems to
absorb i of the force. The proportion of deep water is very small.
The Mediterranean standard of rates of depths of ocean to
height of tide along its coasts, seems to match more with
Pacific and west*coast-of- America standards than with the obser-
vations on the eastern Atlantic coast. The European tides seem
exi^gerated, even when compared with the east coast of America*
This may be explained by less diffusion c£ tidal force and the
contour of the sea- bottom on our coast being more favourable
to receiving impulses giving velocity to the coast-water than
that on the east coast of America. For want of space I have
hardly been able to allude to the solar influence of the tides,
which differs in some respects from the lunar relations.
Hie diurnal and semidiurnal tides are known to vary about
4 inches in an 8-feet tide. Then, supposing that 2 feet of the
8 feet is caused by solar attraction, the variation is one fifteenUi
of the height due to lunar action. If the tide generated in deep
water is twelve lunar hours reaching a part of the coast, the greater
alternate twelve-hours' tide will become the lesser of tl^ two.
There are many other considerations to take into account which
materially modify the sise of the alternate tides at different parts
of the month ; and I do not put forward mv own view with any
pretensions to improve the prediction of tiaes, which indeed is
already perfectlv done by the machine invented by Sir W.
Thomson and Mr. E. Roberts of the Nautical Almanac Office.
What I wish to do is to give an explanation of a theory of the
tides which shall accord with the physical facts. Supposing
the point E is thirty diameters of the earth from the moon on
any day, then the point W will be 81. Then, the attraction
* In the Admiralty Tide Tables there are odI^ tides at tea placet in the
Meditemuiean recorded. The highest spriag tide is 7 feet, and the ave-
rage 4*3 feet. Admiral Spratt, F.R.S.» has just iafomed me that the
average of all spring tides in the Mediterranean is firom 9 to 10 inches,
perceptible within three days of the highest tide. It is evident to me that
the tide in that tea is generated in hasms^ so that it is diffused in getting
to the coast, by which ) of the proper height must be lost.
Digitized by VjOOQ IC
Mr. A. Tylor on Tides and Waves. 215
being inversely as the square of the distance, the force at E will
be to that at W as 31^ to 30S or as 961 to 900 (that is, one
fifteenth greater) . This calculation ought to agree with obser-
vation at ports where the variation in height each alternate tide
is eliminated from other disturbances, and where there are no
exceptional circumstances, if this is a correct explanation of the
difference between the height of the diurnal and semidiurnal
tides (which 1 term the near-side and far-side tides).
The luni-solar attraction-rays in passing through the earth
may encounter changes from fluid to solid substances having
surfaces not at right angles to the incident ravs ; and the rays
would not then follow straight lines, although I have for con-
venience represented them as straight in fig. 4, PI. IV.
Those rays passing throi^rh the higher parallels of latitude
far from the centre might aflfect the tides apparently in an irre-
gular manner. These changes of direction might explain why,
in order to predict with great accuracy the height and time of
the tide at some stations, Sir W. Thomson and Mr. £. Roberts
have been obliged to employ twenty-seven fictitious stars instead
of only the number to express the effects of the moon and sun's
various positions.
The different currents that occur, causing different establish-
ments at ports near each other, seem to indicate movements of
masses of water apparently at different angles to each other.
These motions can be illustrated by an experiment in the injector.
In the water-pipe, at right angles to the body of the injector
(where steam is at 101 lbs. pressure), there is a partial vacuum,
say equal to 2 inches of water. I find that the motion of the
steam will increase its own pressure 1 lb. by friction against the
metal instrument. The steam travelling with great velocity de-
flects the water-current and bends it into its own direction, and
forces water into the steam-boiler, where the pressure is 100 lbs.
The water-pipe is all the time open to the atmosphere and to
the boiler two ways through the injector; but little steam
escapes through the open water-pipe. The barometer is another
instance. The column of mercury ought to lengthen if that
instrument registered the absolute weight of the atmosphere
alone, when the column of air is loaded with vapour. The mo-
tion of the vapour in the act of condensing, however, generates
currents and produces motion of particles in a direction across
the column. This reduces the pressure of the column on the
cistern of the barometer; and therefore the column shortens
for motion instead of lengthening for weight. Motion in
main water-pipes reduces pressure in branches where there is
no motion.
Currents in motion in different directions, owing to different
temperatures or other causes, affect the tidal currents materially,
Digitized by VjOOQ IC
216 Mr. A. Tylor an Tides and Wooes.
and prevent the tide-gauge ever r^stering the tidal inflaencea
alone at any point. This is the cause of different establishments
at neighbouring ports apparently in similar position as regards
the luni-sokr influences.
Fig. 1 shows that the area of the gap formed when the wsfe
F.M L//VC5 Of HOAIZONrAL FORWARD MOTION OF PARTICLES WITH VERTICAL MOTION.
V.M Lines of veat/cal motion of particles without horizontal motion.
B.M LtNES OF HORIZONTAL BACKWARD MOTION OF PARTICLES WITH VERTICAL MOTION
was generated is the limit of horizontal movement of particles
throughout the run of that wave. Experiments show that if
waves artificially produced for experiments continue the same
height their velocity diminishes^ and if their height diminishes
they may keep up their velocity. It is impossible to keep up
both the velocity and height of any wave a long distance. If it
were possible it would involve perpetual motion, as the wave is
resisted by the air above and by the water in which it vibrates.
Let t^ represent velocity of the motion of a wave measured in
feet and the time (a second) in which its crest passes a fixed point,
and p the depth of the water in feet ; then by means of the for-
mula v^S^yp the actual velocity found by experiment may be
{predicted as accurately as by the usual formula t;=\/^A^. The
atter formula appears extremely incorrect for great depth, as it
indicates impossible velocities for waves. If the depth of the
Atlantic was 21,952 feet, the greatest velocity that could by any
means be given to a wave wouldbe 84 feet per second^ or 58
miles per hour; for if vsa\^Sp, then from this we have
84=8v^2l952, that is, 84 feet per second is the maximum ve-
* The gravity formula, v*j=2gh, only applies where there is no resistance
to motion. It is of no use in cases of uniform motion. My new formula
(page 205) gives the due effect of weight on velocity. Thus in a river or
a glacier with sixty-four times the quantity (or weight^ flowing or sliding,
the velocity would increase four times at the same slope. "jHiis law ex-
plains why in the glacial period frozen rivers reached such low levels, and
why denudation was so lar^ in the pluvial period, as destructive effect is
in a high ratio to the velocity.
Digitized by VjOOQ IC
Mr. A. Tylor an Tide$ and Waves. 217
loeity of the wave, instead of the impossible velocity of 800 miles
per hoar suggested by some authors.
An earthquake might transmit a blow through the deep water
in the ocean at six miles per minute, as a wave was formed at
Barbadoes 8000 miles from the supposed origin of the shock in
585 minutes after it was observed at Lisbon. Michelle in 1755
wrote '^ when the bar at the mouth of the Tagus was seen dry
from shore to shore, then suddenly the sea, like a mountain, came
rolling in/' When this blow struck a distant coast below the level
of the sea, it would be reflected and cause the sea to ebb from the
coast first. Then when the force which heaped up the water away
from the shore diminished by work done upon the water in raising
up the level of the sea, a great wave would be moved shorewards
by gravity. The first announcement of the approach of an
earthquake- wave is the ebb of the water'*', not a surface- wave.
If a great surface-wave were generated by an earthquake, it
would not travel veiy far, but would soon diminish in height
and speed, and would not be preceded by a wave in an opposite
direction.
In some careful experiments in a course of one fifth of a mile t
a surface-wave lost five sixths of its height. A powerful shock
or impulse could possibly be communicated through deep water,
like a blow through a solid body, an immense distance with
great velocity ; but that is not the case of a surface-wave at all.
There is, therefore, a great distinction between primitive tidal
impulses and the secondary waves that accompany or follow
them, or the movements in coast-water produced at distant places
and times by means of the composition of forces. The tidal im-
pulse is communicated rather in the manner motion is conveyed
from a steam-engine through mechanical gearing, such as drivers
and followers, and where there is lost time and lost motion be-
tween the teeth of the driving-wheels, or bands and pulleys, or
levers, or other parts of the apparatus through which the move-
ment is communicated from a prime mover to some distant
point.
Thus the piston may have commenced its down-stroke before
the effect of the former up-stroke had reached the extremity of
the shafting. This lost motion is very perceptible in figs. 1 and
2, Plate II., and fig. 1, Plate III.
The particles of water may revolve along their axes ; or all the
vibrations may not be effective, some of them neutralising others,
and for a short time destroying the impulse of the central tide-
generating force, soon to be renewed.
The hours at which high water arrives are written against the
♦ MicheU, Phil. Trans. 1766.
t Brit. Assoc. 1838, p. 465.
Digitized by VjOOQ IC
218 Mr. A. Tylor on TideM and Waves.
names of the towns situated on the coast or river-bank in Plates
II. and III.
In fig. \, Plate II.j a point is assumed in the Atlantic 800
miles from the Land's End, where the high- and low-water level
is assumed to be invariable, and where the mass of the ocean
water is supposed to move east and west very slowly in alternate
and opposite directions in each tide.
When the flowing tide is moving a ship 8 miles an hour, there
is 360 miles difierence in distance, and 6 hours' time, between
high water at Plymouth and Dover ; therefore the lost motion
is 18 miles out <^ 860, or 5 per cent. The impulse received at
Plymouth from the central slowly moving oceanic water must
have been transmitted through the deeper water at a much
higher rate, but only reaches Dover after travelling at 60 miles
an hour. Then the impulse is transmitted from Dover to Lon-
don at the rate of 120 miles in three hours, or 40 miles an hour,
the tide only taking a ship 9 miles in 8 hours ; so that the lost
motion is 9 miles out of 120, or 7 per cent., the difference of
time between Plymouth and Dover (21 minutes) not being taken
into account.
I have allowed a slope of 1 foot in Plates II. and III. to bring
the water to the mouth of the Clyde, and 5 feet to bring the water
to Falmouth from the Atlantic
If the level of the ocean were kept up above its due level only
2 inches between the western and eastern boundary of the
Atlantic deep wator^ that slope would suffice to create a current
of 8 feet per minute in the whole mass of deep water. This is
supposing the law of velocity followed the ratio I observe in
smaller cases. If the two inches were only water heaped up in
consequence of, or by the hmi-solar attraction, it would create
no current at all while that attraction continued.
As the effect of the moon on the oceanic water is only eqoal
to that of a sphere of 118*75 miles in diameter, equal in mean
density to the earth, placed near and revolving about C in a lunar
day, it occurred to me that some geological difficulties, such as
the evidence in the Crag and Quaternary deposits of the tides in
the Quaternary period being three or four times as large as at
present, might be explained by periodic changes of position
of part of the interior of the earth, rather than by supposing
great changes in the distance of the moon from the earth. Also
the quantity of water in the ocean can only be the difference
between that of the vapour held in the atmosphere or condensed
into snow or ice on the land, and the quantity of water or vapour
of water mechanically or chemically combined with the strata of
the earth. These are Quantities capable of enormous variation in
geological periods under different conditions. There is also a
Digitized by VjOOQ IC
Mr. A. Tylor on Tides and Waves. 219
periodicity about the alternation of land and water surfaces,
particularly in the Carboniferous period^ which might be ex-
plained by slow changes in long intervals of the disposition of
the solid and fluid internal substance of the earth with regard
to and about its centre.
A slow circulation of an eccentric mass of fluid may occur in
the interior of the earth, and gases may periodically pass from one
part of the solid portion to another, their place being supplied
by fluids, attracting the ocean unequally.
Unequal attraction from variable subterraneous inequalities
would affect different points of the surface and raise the water-
level on one part for long periods and depress it on alternate and
opposite points to an equal extent. The theory of inconstancy
of rainfall and of fluctuation of the sea-level in ^logical periods
is gaining ground since I first advanced these views (in 1858) in
this Journal, in a paper entitled ^' Fluctuations of the Sea4evel
in stated Periods of Time."
We must not gauge our interpretation of nature by the pre*
sent temperature, rfonfall, or tide-gauges^ but from the actual
evidence presented in the strata themselves.
In conclusion, if all the lines of Itmar attraction M^ M^ &c.
(flg. 4, PI. IV.) were continued through the earth without deflec-
tion from a straight line, then there could be only one lunar tide ill
the twenty-four hours; for all the water on one side of the axial
line, E G W or half the globe, moving in the direction of the ro-
tation of the earth, would be accelerated, and all the water in the
other half,E B W, of the globe would be retarded, a^ th^ attraction
of the moon in that half would be contrary to the direction of the
rotation of the earth. The fact of the tides occurring ^v^ry twelve
hours is a proof that the view J have put forward of the defleo*
tion of the attracting rays in their passage through the earth is
a correct one. The twelve-hour tides on the opposite side of the
earth to the moon are physical proofs that att»*action-rays are de-
flected. If not, there could be no such effect of attraction on th^
ocean as is shown by the twelve-hour tide. The theoretical
differences of one fifteenth of the height of alternate tides I
believe accord with observation, taking the average of the world.
According to Professor Stokes, any solution of a problem that
satisfies all the conditions must be the true one. I believe
the solution suggested in this letter conforms entirely to the*
facts, and that the deflection-theory, now, I believe, first pro-
posed, is true. YourB truly,
A. Tylor.
P.S. With regard to the new equations to the flow of water
in page 305, 1 use coefficients for different materials of channels :
see note to PI. III. fig. 3.
Digitized by VjOOQ IC
[ 220 ]
XXXII. Proceedings qf Learned Societies.
ROYAL SOCIETY.
[Continued from p. 153.]
February 6, 1874. — Joseph Dalton Hooker, C.B., President, in
the Chair.
n^HE following c<Mnmunication was read : —
^ ** On a Self-recording Method of Measuring the Intensity of
the Chemical Action of Total Daylight.** By H. E. Eosooe, F JI.S.
The object of the present communication is to describe an instru-
ment by which the varying intensity of the chemically active rays,
as affecting chloride of silver paper of constant sensitiveness, can be
made self-recording. The method described by the author in the
Bakerian Lecture for 1865, although it has been the means of
bringing into notice many impor^mt tscta concerning the distribu-
tion of the sun^s chemical activity throughout the atmosphere, as
well as in different situations on the earth's surface, has not as yet
been introduced as a portion of the regular work of meteorological
observatories, owing to ihe hxt that, in order to obtain a satis&o-
tory curve of daily chemical intensity, at least hourly observations
need to be made, and this involves the expenditure of more time
and labour than it has been found possible to give. In the pre-
sent communication a method is described, which, whilst preserving
untouched the principles and accuracy of the former method, re-
duces the personal attention needed for carrying out the measure-
ments to a minimum, and thus renders its adoption in observatories
possible.
According to this plan, a constant sensitive paper is exposed by
a self-acting arrangement for accurately known times, at given
intervals throughout the day. The insolation apparatus stocked
with sensitive paper is placed in position either eany in the morn-
ing of the day during which the measurenients have to be made, or
on the previous night, and by means of an electric communication
with a properly arranged clock, the sensitive paper is exposed every
hour during; the day, so that, in the evening, the observer has only
to read off, in the ordinary manner, the hourly intensities which
have been recorded on the paper during the day.
This self-recording arrangement, though apparently simple, in-
volves points which mive rendered its successful completion a some-
what difficult matter, owing, in the first place, to the great varia-
tions which occur in the chemical intensity of total daylight in
different places, at different times of the day, and in different pe-
riods of the year ; and secondly, owing to the fact that, in oraer
to be able to estimate the chemical intensity, the coloration ac-
2uired by the paper must reach, but not much exceed, a given tint,
t becomes necessary therefore that on each occasion when an ob-
servation is needed, the sensitive paper should be exposed me-
Digitized by
Google
Royal Society. 221
chanically, not once, but for several known but varying intervals
of time quickly succeeding each other ; so that whatever may be
the intensity of the total daylight (supposed during these intervals
to remtdn constant), some one ajb least of the several expose^
papers will possess the requisite shade. This is accomplished by
a duplicate arrangement of a clock and insolation-apparatus, by
means of which disks of the constant sensitive paper are exposed
each hour for successive known intervals of time, varying from two
to thirty seconds. After an interval of an hour, another set of
• disks are exposed for the same series of intervals ; and these series
of insolations are repeated once every hour during the day. The
mechanical arrangements for effecting this with accuracy are fully
described in the paper. On unrolling, at the end of the day, the
strip of sensitive paper which has served for the exposures, black
disks showing where the paper has been stationary for the hour
are seen ; and between each of these are found ten ordes variously
tinted, from that, probably, scarcely visible, which was exposed for
two seconds, to that, perhaps too dark to read off, which was inso-
lated for thirty seconds. Amongst these, some one at least, will
be found of such a shade as to enable it to be read off by the mo-
nochromatic soda-flame, on a graduated fixed strip, as described in
former communications.
A new method of calibrating the fixed strips of standard tints
necessary for these measurements is next described ; and the ques^
tion as to the possibility of preparing constant sensitive paper in
long strips instead of in large sheets is next experimental^ dis-
cussed, the result of the examination being that it is possible to
prepare silvered paper in long narrow strips such as are used in
Morse's tel^raph-apparatus, so that it shaU throughout its length
preserve the standard sensitiveness.
The time during which the disks of constant sensitive paper are
exposed is next ascertained for each instrument by a chronc^raph.
During wet weather the insolator is covered by a semicircular
glass shade ; and the value of the coefficients for refraction and
absorption due to- this glass shade is determined.
The latter portion of the communication contains the results of a
deries of comparisons of the curves of daily chemical intensity ob-
tained (1) with the hand-insolator, and (2) with the self-recording
instrument. Comparisons of this nature were made during the
months of May, June, and July, 1873, by simultaneous hourly de^
terminations in the neighbourhood of Manchester according to both
methods. Of these observations, six full days are selected ; and the
tables and curves accompanying the communication show the close
correspondence of both sets of observations. The integrals of total
chemical intensity for these days are also given, and exhibit as close
an agreement as, from the nature of the experiments, can be ex-
pected.
Digitized by VjOOQ IC
222 Rnyal SoeUty :—
Feb. 12. — Joseph Dalton Hooker, C.B., President, in the Chair.
The following communication was read : —
" On the Division of a Sound- Wave by a Layer of Flame or heated
Gas into a reflected and a transmitted Wave." By John Cottrell,
Assistant in the Physical Laboratory of the Royal Institution.
The incompetency of a sound-pulse to pass through non-homo-
geneous air having been experimentally demonstrated by Dr. Tyn-
daU, and proved to be due to its successive partial reflections at the
limiting surfaces of layers of air or vapour of different density,
further experiments were conducted in order to render visible the '
action of the reflected sound-wave.
The most successful of the various methods contrived for this
purpose consists of the following arrangement. A vibrating bell
contained in a padded box was directed so as to send a sound-
wave through a tin tube, B A (38 inches long, 1 1 inch diameter),
in the direction BF, its action being rendered manifest by its
causing a sensitive flame placed at F* to become \iolently agitated.
The invisible heated layer immediately above the luminous por-
tion of an ignited coal-gas flame issuing from an ordinair bat's-
wing burner was allow^ to stream upwards across the end of the
tin tube B A at A. A portion of the sound-wave issuing from the
tube was reflected at the limiting surfaces of the heat«d layer ;
and a part being transmitt-ed through it, was now only competent
to slightly agitate the sensitive flame at F.
The heated layer was then placed at such an angle that the re-
flected portion of the sound-wave was sent through a second tin
tube, A F (of the same dimensions as B A), its action being ren-
dered visible by its causing a second sensitive flame plaodd at the
end of the tube at F to become violraitly i^ected. This action
continued so long as the heated layer intervened; but upon ite
withdrawal the sensitive flame placed at F, receiving the whole of
the direct pulse, became again violently agitated, and at the same
moment the sensitive flame at F, ceasmg to be affected, resumed
it« former tranquillity.
Exactly the same action takes place when the luminous portion
of a gas-flame is made the reflecting layer ; but in the experimente
above described, the invisible layer above the flame only was used.
By proper adjustment of the pressure of the gas, the flame at F
can. be rendered so moderately sensitive to the direct sound-wave.
Digitized by VjOOQ IC
Mr. Donkin on the Contrition of two Harmonie Curves. 223
that the portion transmitted through the reflecting layer shtAi be
incompetent to affect the flame. Then by the introduction and
withdrawal of the batVwing flame the two sensitive flames can be
rendered alternately quiescent and strongly agitated.
An illustration is here afforded of the peif ect analogy between
light and sound ; for if a beam of light be projected from B to F",
and a plate of glass be introduced at A, in the exact position of the
reflecting layer of gas, the beam will be divided, and one portion
will be reflected in the direction A F, and the other portion trans-
mitted through the glass in the direction F*, exactly as the sound-
wave is divided into a reflected and a transmitted portion by the layer
of heated gas or flame.
Feb. 19. — Joseph Dalton Hooker, C.B., President, in the Chair.
The following communication was read : —
'* On an Instrument for the CompoBiticm of two Harmonic
Curves.'' By A. E. Donkin, MA., F.iLa.S., Fellow of Exeter Col-
l^;e, Oxford.
The interest in such compound curves lies in the fact that, as a
simple harmonic curve may be considered to be the curve of pres^
sure on the tympanic membrane when the ear is in the nei^bour*-
hood of a vibrating body producing a simple tone, so a curve com-
pounded of two such simple harmonic curves will be the carve of
pressure for the consonance of the two tones which they severally
represent, and thus the effect on the ear of different oonsonances
can be distinctly represented to the eye.
If the motion of a point be compounded of rectilinear harmonic
vibrations and of uniform motion m a straight line at right angles
to the direction of those vibrations, the point will describe a simple
harmonic curve.
Thus a pencil-point performing such vibrations upon a sheet of
paper moving umformly at right angles to Hkeir direction would
oraw such a curve.
The same kind of curve would also be drawn by keeping the
pencil fixed and by giving to the paper, in addition to its continuous
transverse motion, a vibratonr motion similar and parallel to that
whidi the pencil had ; and ii ihe motion of the latter be ndw re^
stored, a complicated curve will be produced whose f onn will depend
on the ratio of the numbers of vibrations in a given time or the
pencil and paper, and which will be the curve m pressure for the
interval corresponding to this ratio.
The manner in which these three motions are combined in the
machine is as follows : — ^Two vertical spindles, A and B, revolving
in a horizontal plate carry at their lower ends each a crank, 0 and
D, and at their upper ends each a wheel cut with a certain number
of teeth ; these two wheels can be connected by means of an inter-
mediate one, as is seen in the figure ; and since either wheel of the
pair can be replaced by another with a different number of teeth, the
relative angular velocities of the spindles can be regulated at plea-
sure. The paper upon which the curve is to be drawn is carried upon
Digitized by VjOOQ IC
224 Roifal Society :— Mr. A. E. Donkin on an Instrument
a rectangukr frame, E F G H, capable of sUding boriax)ntally up and
down in a direction parallel to that of the plane passing througli the
spindles. This frame has a pair of rollers, E F and G H at eax^b end
connected by tape bands, between which the paper passes as t^^ ^^'
lers turn. In order to give a motion of reyoiution to the roH^^^' *
wheel, L, is fixed upon the axis of one of them whose teet>li Sl^
Digitized by VjOOQ IC
for the Composition of two Harmonic Curves. 225
into those of a pinion, P Q, alongside which the frame slides, and
which is itself driven by one of the vertical spindles. A connecting-
rod, D M, is carried to the frwne from the crank of this spindle, so
that upon turning the latter a vibratory motion is given to the
former ; and since the transverse motion of the paper aJso d^jends
upon the same spindle, a fixed pencil-point resting on it would
draw a simple harmonic curve whose amplitude would depend on
the radius of the crank, and wave-length on the transverse speed of
the paper, which can be regulated at pleasure by means conj^ived
for the purpose*.
A vibratory motion similar and parallel to that of the frame is
^ven to a small tubular glass pen, E, so arranged as to move with
its point lightly resting upon the paper. This motion is commu-
nicated by a connecting-rod, C N, from the other crank, which is
carried underneath the sliding frame and jointed to the lower end
of a small vertical lever, S, to whose upper end the arm carrying
the pen is attached.
The weight W serves to regulate the pressure of the pen on the
paper, as it can be screwed in or out. T is merely a pillar upon
wluch the change-wheels can be placed for convenience.
If the pair of wheels on the spindles are now connected by the
intermediiftte one, it is plain that, upon turning either of the spin-
dles by a winch provided for the purpose, the two motions of the
paper will be combined with that of the pen, and the curve drawn
will be that composed of the two simple harmonic ones which
would be the result of separately combining the harmonic vibrations
due to each crank with the transverse motion of the paper. Thus, if
m and n are the numbers of teeth on the pair of wheels respectively,
the equation to the resultant curve will be
y=sin ww7-f sin nx.
This equation implies not only that the radii of the cranks are the
stune, but also that they start parallel to each other and at right
angles to the vertical plane passing through their axes : both these
conditions can, however, be altered ; and therefore the general form
of equation to the curves which the machine can draw will be
y=a sin (ww?-fa)-f6 siu (wa? + /3),
where a and h are the radii of the cranks, and a and ^ are depen-
dent on their relative inclinations to the above-mentioned vertical
plane at starting.
As an example, suppose that a =6, while the ratio of m to n is as
2 to 1 ; then the above equation will represent the curve of pressure
for the octave. Similarly, ifmistonasl6 to 15, the resultant
* It BhouM be observed here that the vibratory motion thus given to the fVame
is not truly barmonic. In order to make it so, a more complicated contrivance
tban the simple crank and connecting-rod would bave to ue adopted ; but this
would probably introduce, through unavoidable play, an error greater than the
present one, the length of the connecting-rods and Uie small size of the cranks
rendering the latter nearly inappreciable. The motion will, however, for the sake
of convenience, be considered truly harmonic throughout
Phil Mag. S. 4. Vol. 4«. No. 317. Sept. 1874. Q
Digitized by VjOOQ IC
226 Royal Society.
curve represents the effect on the ear of a diat<Hiic semitone, while
the ratio 81 to 80 would give that of the comma. In hoth these
curves, and more especially in the latter, the beats which would
ensue on actually sounding the two tones together are shown with
lemarkable distinctness.
As the machine is provided with a set of change-wheels, many
different curves can be produced, while ihe form of leach can be
more or less changed by altering the relative positions of the
cranks before bringing the idle wheel into gear. It is also possible
to obtain very large values of m and n in the above equation by
using two idle wheels on the same axis, which shall come into gear,
the upper one with the wheel on the one spindle, the lower one with
that on the other.
Thus, suppose A and B are the numbers of teeth on the spindle-
wheels respectively, C and D those on the idle wheels, ana let A
BC
gear with C and D with B ; then — s -r^ . Now, by properly
n AD
choosing the four wheels, large values of m and n may be obtained.
If, for instance, A=81, B=80, C=55, and D-27, - =^^ ; this
n 2187
2
ratio being nearly = -, the corresponding curve will represent the
effect of an octave slightly out of tune. The period of such curves
as these being very long, it is necessary to have a good supply of
paper ; and this is arranged by carrying a reelf ul on the horizontal
frame, from which it is slowly unwound between the rollers. The
rate at which this takes place has a good deal of influence on the
form of the resultant curve ; the slower it is, the more compressed
will the latter appear. Instead of using paper, the curves, pro-
vided the periods are short enough, may be drawn on slips of black-
ened glass, which can be carried along between the tapes connecting
the rollers ; they can be at once pUced in a lantern and thrown on
a screen.
The width of contour of any curve depends on the radii of the
cranks : these may have any value between 0 and half an inch ; and
therefore the limit of possible width at any part will be two inches ;
so also, by altering the radii, a series of curves may be produced
corresponding to the consonances of tones not of the same inten-
sities. Since the maximum width of any curve will be double the
sum of the radii of the cranks, the paper is cut to a width of two
and a half inches, within which all curves which can possibly be
drawn will be comprised.
The instrument is constructed by Messrs. Tisley and SpiDer, of
Brompton £oad, to whom some improvement upon the original
model it due.
Digitized by VjOOQ IC
Geological Society. 227
QEOLOOICAL SOCIETY.
[Continued from p. 155.]
November 19, 1873.— Prof. Ramsay, F.R.S., Vice-President,
in the Chair.
The following commnnications were read : —
1. ** Supplemental Note on the Anatomy of HypsHaphodon
Foxii:' By J. W. Hulke, Esq., P.E.S., P.G.S.
The material for this note was a slab from Cowleaze Chine, oon-
taining portions of two indiyidoals of HypsUophodon Foxii—one con*
sisting of a skull with a great part of the vertebral column, the
other of a portion of the vertebial column. The author described
some details of the structure of the skuU, and especially the palatal
apparatus. The pterygoids, which are not mesially joined, have a
stout body, the posterior border of which bears a very large basi-
sphenoidal process ; and the left pterygoid retains the root of a strong
quadratic process, in front of which the hollow outer b<Nrder runs out
into an ectopterygoid. In front of the pterygoids the palatines are
partially visible, also separated by a fissure. Of the eight vertebrae,
the last three are firmly anchylosed, and the seventh and eighth
form part of the sacrum. They are constricted in the middle ;
and their transverse processes, which spring from the junction of
two vertebrsB, are bent backwards, joiniog the dilated outer end of
the trausverse processes of the next vertebra, including a laige sub-
circular loop. The second fragment of a vertebral column, which
belonged to a smaller individual, includes the sacrum and several
vertebrcB. Near the skull the slab contains several very thin bony
plates of irregularly polygonal form, regarded by the author as
dermal scutes. In connexion with the question of the generic rank
of Hypsilophodon^ the author stated that in Hyp9ihphod(m the
centra of the sacral vertebrae are cylindroid and rounded below,
whilst in Iguanodon they are compressed laterally and angulated
below.
2. " The Drift-beds of the North-west of England.— Part 1, Shells
of the Lancashire and Cheshire Low-level Clay and Sands." By T.
Mellard Eeade, Esq., C.E., F.G.8.
The author commenced by explaining a section in a cutting at
Booth-Lane Station, in which most of the beds seen about Liverpool
are typically represented. This section shows in ascending order : —
1. Pebble-beds of the Trias ; 2. shattered rock.; 3. compacted
red-sand rubWe (ground moraine) ; 4. lowest bed of Boulder-clay
(largely composed of red sand); 5. stratified sand, with shell-
fragments ; 6. bed of fine unctuous clay ; 7. brick-clay (with many
shells) ; 8. sand-bed ; 9. stratified yellow sand (" Washed Drift
sand").
The author next gave a list of the loealities in which shells were
found, and stated that in all forty-six species had been met with
distributed through the day-beds, those found in the sand-seams
being rare and generally frtigmentary and rolled. The shells mobt
Q2
Digitized by VjOOQ IC
228 Geological Socieiy :—
commonly found entire are usuallj of small tjiize, and of a form cal-
culated to resist pressure, — such as TurriteUa communis, Trophon
daihratus, and Mangelia turricula, Pusus antiqutM and Buccinum
undatum are generally represented only by worn fragments of the
columella; and Cyprina islandica is always found in fragments.
The author thought that the association of the various species dis-
tributed without order through the clays shows that they could not
have lived together on the same bottom, but that they must have
been to a great extent transported. He contended that the ad-
mixture of shells in the Boulder-clay was due to tbe tendency of the
sea to throw up its contents on the beach, whence changing cur-
rents and floating ice might again remove them, and to the oscilla-
tions of the land bringing all the beds at one time or another within
reach of marine erosive action. He maintained that it is in the
distribution of land and sea at the period of deposition of the Lan-
cashire deposits, and not in astronomical causes, that we must seek
the explanation of the climate of that period, the conditions of which
he endeavoured to explain by a consideration of the proportions of
the species and the natural habitats of the shells found in the drifts.
3. " Note on a deposit of Middle Pleistocene Gravel near Ley-
land, Lancashire." By R. D. Darbishire, Esq,, F.G.8.
The bed of gravel, about 40 feet thick, and about 240 feet above
the level of the sea, is covered by yellow brick clay, and overlies an
untried bed of fine sea-sand. The shells dhd fragmens occur chiefly
at the base of the gravel.
The most noticeable shells in this list of forty-two species, col-
lected by Miss M. H. Farington, were Panopoea norvegica, Macira
glauca, Cyiherea chione, Cardium rusticum, Fusus propinquuB, and
Fusus antiqutts, var. contrarius. One specimen of a Fmus, doubt-
fully identified as F. Fabricii (craticulatus), had occurred.
The group was by no means characteristically Arctic or Glacial.
It represented most nearly the Wexford lists, especially in present-
ing the reversed Fusus, and might be regarded as connecting those
beds with the Macclesfield drifts, also containing a Celtic assortment,
with Cytherea chimie and Cardium rusticum.
The author considered the Leyland deposit, like those on the west
of the Derbyshire hills, to be more probably littoral and truly cli-
matic than that of the Liverpool clays, the subject of Mr. Keade's
Paper, and hazarded the conjecture that the latter were sea-bottom
beds, into which, during some process of degradation and redistri-
bution, the specimens found and enumerated by Mr. Keade had been
carried down from the former more ancient retreating coast-lines.
December 3rd, 1873.— Joseph Prestwich, Esq., F.R.8.,
Vice-President, in the Chair.
The following communications were read : —
1. '* Notes on the Structure sometimes developed in Chalk.'' By
H. George Fordham, Esq., F.G.S.
After referring to Mr. Mortimer's paper on tbe same subject (see
Digitized by VjOOQ IC
Mr. R. PiDchin on the Geologg of the Cape of Good Hope. 299
Q. J. G. 8. vol. xxix. p. 417), the author stated that in a pit near Ash-
well the ** Lower Chalk without flints *' exhibits a bed of a concre-
tionary nature, the concretions in which are marked nearly all over
with lines. The lines are found only on the concretions and in their
immediate neighbourhood. The fossils in the bed are invariably
crushed, as if by pressure. The author believes that the strisB are
due to an incipient crystallization arising from the formation of the
concretions ; and in support of this view he adduced a specimen of
iron pyrites from the chalk of Beachy Head, attached to which is a
small portion of very hard striated chalk, and suggested that the
crystallization of the pyrites had induced a crystallization in the chalk.
He considers, however, that in some places an almost identical
structure may be due to slickensides, but only in very broken and
faulted beds.
2. " A short description of the Geology of the Eastern Province
of the Colony of the Cape of Good Hope." By R. Pinchin, Esq.,
C.E. Communicated by H. W. Bristow, Esq., F.R.S., F.G.S.
In this paper, which was illustrated by maps and sections, the
author gave the results of his observations on the geology of the
above region. The two principal sections described were fiim Cape
Saint Francis, across the Great Winterhoek and Langeberg ranges, to
the lacustrine Triassic rocks near Jansenville, and from Port Eliza-
beth to Somerset. The lowest rock in the first section is the quartzite
of the Great Winterhoek, which is immediately overlain to the
northward by day-shales and sandstones containing Devonian fossils.
Beds with similar fossils occur at the Eromme river, Cape St.
Francis, and near Uitenhage. A patch of horizontal secondary
strata stretches west from the Gamtoos river, overlying the Enon
conglomerate in the same way as the Jurassic strata of Uitenhage.
They contain no fossils. The Enon conglomerate is seen on the
flanks of the higher hills. The northern ranges, Langeberg, Elein
Winterhoek, and Zuurbergen, are regarded by the author as formed
of rocks belonging to the Carboniferous series, although closely
resembling those of the Great Winterhoek in lithological character,
except that among them are bands of the peculiar rock described by
Bain as " Claystone porphyry," by Wyley as a ** Trap conglomerate,'*
by Tate as a " Trap-breccia," and by Atherstone as an " intrusive
Trap." Eubidge regarded it as a metamorphic rock ; and this view
is adopted by the author, who describes it as underlying and over-
lying the clay-shales, which always separate it from the quartzite,
and as passing imperceptibly into the clay-shales. The mottled
sandstone or Ecca rock is referred by the author to the Carboni-
ferous series. The author also noticed the occurrence of Tertiary
or recent rocks containing remains of Mollusca identical with
species now living in the adjacent seas, lying unconformably upon
the Devonian, and conformably upon the Secondary rocks at various
places near the coast.
Digitized by VjOOQ IC
230 Geological Society.
S. '* On the Mad-craters and geological structore of the Mekran
Co^." By lient. A. W. Stiffe, F.R.A.S. Communicated by Prof.
Ramsay, F.R.8., V.P.G.S.
The coast of Mekran, extending from near the western frontier of
India to the month of the Persian Gulf, was stated by the author to
be a nearly rainless district, consbting of clay plains with pre-
cipitous tabular hills, the former veined here and there with crystal-
line gypsum, the latter composed of clay capped and sometimes
interstiutified with coarse, friable, fossiliferous calcareous strata,
from 5 to 30 feet thick, supposed to be of Miocene age, and all
horizontal or nearly so, except at the extreme east and west, where
the strata are inclined at an angle of frt>m 40^ to 60^. Along the
coast there are no distinct traces of volcanic action; but on the
north coast of the Persian Gidf a similar formation has been much
disturbed by the protrusion of recent volcanic material, near J&shak
to the west there is a hot mineral spring, and near Ear&chi there
are springs of pure hot water. The author described the mode in
which denudation is effected in this region by occasional heavy
rains, and by the constant action of the sea upon the coast, and then
noticed the occurrence, within a few miles of the shore, of numerous
peculiar mud-craters, forming hills varying in height fr^m 20 to
300 or 400 feet above the plain, of a regular conical form, with
truncated tops, and the sides sloping at an angle of about 40^. The
summits of these hills present a circular cup with a narrow border,
filled with semifluid mud, which occasionally flows slowly over the
margin of the crater. The author considered that the conical hills
have been formed solely by these overflows. He believed that a
small shoal occurring off the coast near Jdshak might be produced
by one of these craters, and was inclined to ascribe their existence
to hydrostatic pressure rather than to volcanic action, especially as
by tiie concurrent testimony of several natives the discharge from
the craters b greater during spring tides. The thickness of the
clay forming the plain is probably very considerable ; it extends for
some miles from the shore, sinking gradually to 20 or 30 fathoms,
when there b a 'sudden and often precipit<>us descent to a depth
of 300 or 400 fathoms. The author suggested that, since the de-
position of the Miocene beds, the great submarine cliff may have
been raised above the sea, that the land was then depressed to near
its present level, causing the removal of the beds to the present
coast Hue, and that a farther depression followed by upheaval gave
origin to the inland cliffs. Evidence of the last depression is frir-
nbhed by the presence of borings of lithodomous mollusca in the
clifls considerably above the present sea-leveL
Digitized by VjOOQ IC
[ 231 ]
XXXIII. Inteliigence and Miscellaneous Articles.
ON THB LIGHT RBFLKCTED BY PERMANGANATE OF POTASSIUM.
BY DR. EILHARD WIEDEMANN.
PROFESSOE STOKES* observed that in the spectrum of the
light reflected from solid permanganate of potassium dark
streaks oecur^ and that they are exhibited most distinctlj with a
certain angle of inetdenee ; further, the minima of brightness in i^e
speetnim of the reflected light correspond to the rays transmitted
in the greatest intensity by the permanganate.
I have pursued this subject further, and examined not only the
lijght reflected at the boundary of permanganate of potassium and
air, but also that at ihe boundary of benzine, sulphide of carbon,
and a mixture of these two substances, and the above salt. More-
over the polarizotioii of the inddent light wa& kept in view. To
obtain the reflecting surfaces, triturated crystals of the salt were
polished upon ground glass plates by means of a jet-burnisher.
Clean surfaces, free from oxide, were thereby secured for the inves-
tigation, which is not the case when whole crystals are employed.
The glass plate thus prepared was inserted in a rectangular hollow
prism (which could be filled with the different liquids) in such wise
that its coated face was turned to the rectftngnlar edge. The pridm
was placed upon a graduated circular table that could be rotated,
and sunlight so thrown upon one of the two surfaces including the
right angle that the light refracted there fell upon the coated plate
and, through reflection, passed out at the other surface. Thence it
arrived at the sHt of a spectrum-apparatus. The angle of incidence
on the coated plate was determined thus : the Mght from the first
surfaee of the prism was reflected back in its own direction ; the
position of the table was then read oSt ; the rotation of the table
with the prism ^es immediately the incidence- angle at the first
surfaee ; from this angle and that between the glass plate and the
first face of the prism, and the index of refraction of the medium
i!n contact with ttie permanganate, the incidence-angle at the latter
can then be found.
The position of the streaks in the specttuM was determined by
means of a photographed scale applied to the spectmm-apparatus,
the cross^threads of the observing-telescope having previously been
placed on the centre of tho dark streak.
These positions with pretty large angles of incidence are given
in Table I. The columns ifi^r A refer to the streaks in the light
polarized parallel to the plane of incidence, those under B to thos6
in the light polarized perpendicular to that plane. The first cohnmi
gives the names of ^e surrounding media. Table II. gives the
positions of the absorption-streaks in the transmitted light. Eraun-
hofer's lines correspond as follows to the strokes on the photo-
graphed scale : —
D:*=Oj B=il8; b^21', F=«33.
♦ Phil. Mag. 1863, vo!. vi. p. 393. Pogg". Ann, 1854, vol. xci. p. 300.
Digitized by VjOOQ IC
232 Intelligence and Miscellaneous Articles.
Tabm I.
A.
Air
1
14
15
16
S9
28i
30
3U
82
87 ;
38i 1 45
894 1 47
Benzine
Mixture of benzine tnd sulphide of carbon.
Snlnhide of eftrhon
! - 1 1
B.
Air
4
8i
m
m
m
u
IS
82 38|
82 38
82 39
82|89i
S'
Benzine
Mixture of benzine and sulphide of carbon.
Sulohide of carbon
Tabls II.
4}, Hi, 18J, 26i, 33^.
These numbers show : —
1. That, with large angles of incidence, the streaks in the light
polarized perpendicular to the incidence-plane, with respect to those
in the light polarized parallel to the plane of incidence, are displaced
towards the olue, and that in the former another streak occurs in
the yicinity of D.
2. That with the increase of the refraction-index of the surround-
ing medium the streaks in the parallel-polarized light undergo dis-
placements towards the blue ; while, on the contrary, in the per-
pendicularly-polarized light the streaks preserve their position un-
changed, or lilter it but Httle. Observation of the streaks in the
blue beyond E is attended with great difficulties, as is the entire
investigation, through the breadth of the streaks and the impossi-
bility of obtaining perfectly reflecting sur&bces.
A comparison oi the streaks obtained in the transmitted and in
the reflected light shows that never do two of such streaks cover
one another, and that neither do the former lie each in the middle
between two of the latter.
As to change of position of the streaks with the angle of inci-
dence, it result^ that in the light polarized parallel to the plane of
incidence, and likewise in natural bght, the position was as good as
independent of the angle of incidence ; but in the light polarized
perpendicular to that plane the streaks have, up to a certain angle
of incidence, which amounted to
Air.
Benzine,
about 62^,
Sulphide of carbon,
about 52°,
the same position as in the paraUel-polarized, and then, with a
small alteration of the incidence-angle, suddenly suffer a disj^laoe-
ment characterized by the appearance of the streak ihe details of
Digitized by VjOOQ IC
Intelligence and Miscellaneous Articles. 233
which are given in the first column under B. Accordingly, for
angles ^eater than those given, the above Tables hold good.
Precisely the same phenomena as on the ground and polished salt
may be observed on crystals. Just so are they exhibited on per-
manganate of ammonia ; but here measurements were impossible,
on account of the great decomposability of the salt.
The above observations were verified in every way possible. For
example, the dependence of the situation of the streaks on the index
of refraction was again established by putting benzine and sulphide
of carbon in layers one above another, immersing a glass plate
coated with polished permanganate of potassium, and comparing
immediately the spectra of the light reflected at the boundaries of
the two media by the permanganate. The streaks in the spectrum
of the fight which had passed through the sulphide of carbon were,
in relation to those in the spectrum of that which had traversed
the benzine, displaced towards the blue. — Poggendorff's AnnaleUy
1874, No. 4, pp. 625^628.
ON THE TEMPERATURE OP THE SUN. BY J. VIOLLE.
I have previously indicated and discussed the method I most
frequently employ in my measurements concerning the temperature
of the sun. I shall today describe the apparatus I use, and shall
develop the calculus of the experiments.
My apparatus is composed of two concentric spherical envelopes
of brass. The interior one, 15 centims. in diameter, constitutes
the enclosure, in the centre of which is the bulb of the thermometer
submitted to experiment. This enclosure, blackened on the inside,
is kept at a constant temperature by a continuous current of water
furnished by the conduit-pipes of Uie city and circulating between
the two balls. The exterior ball has a diameter of 23 centims. ; it
has been carefully polished on its outer surface, and is, besides,
protected by screens which leave free only the admission-aperture.
This aperture is at one of the extremities of a brass tube 17*5 mil-
lims. in diameter, directed along one of the radii of the sphere, and
opening at the other end into the inner ball. The free extremity
of the admission-tube carries a movable diaphragm pierced with
three circular apertures of different sizes. Three other tubes tra-
verse, in radial directions, the space comprised between the two
spheres : two of them, placed one at 45°, the other at 90° from the
admission-tube, serve, the one or the other according to circum-
stances, to give passage to the stem of the thermometer ; the third,
closed by ground and slightly blackened plate glass, is directed
along the prolongation of the admission-tube, and permits the
ascertaining that the solar rays fall exactly on the bulb of the ther-
mometer. The suitable orientation of the apparatus is, besides,
attained without difficulty, thanks to its spherioil form, which per-
mits it to be turned gradually in the wished-for direction upon a
circular ring which serves as its support.
Digitized by VjOOQ IC
234
Intelligence and MisceUanema Articles.
The following is the course of an experiment : — All the tubes
being carefuUy closed, and the thermometer in place, the tempera-
ture (which is stationary if all has been well regulated for a suffi*
dent time) is read ; then the admission-tube is opened after bring-
ing opposite to it such aperture* of the diaphiagpn as is judged
suitable. Now, the apparatus being kept in accurate orientation,
we wait until the temperature again becomes stationary, and then
note the excess shown by the thermometer.
Experiment shows that this excess depends both on the thermo-
meter employed and on the diameter of the aperture of admission.
No precise ccmclusion, therefore, can be drawn from experiments m
which we have not preoccupied ourselves with the dimensions of
the thermometer, and with the magnitude of the admission-ap^ture
pierced in the enceinte, with the temperature constant. On the
contrary, by employing in succession different thermometers and
different apertures of the diaphragm, we can evaluate very accu-
rately : — (1) the cooling due to the contact of the air ; (2) the heat-
ing which proceeds from the radiation of the portion of the sky
bordering the sun and seen at the same time from the bulb of the
thermometer. I shall show this by an example, the data of which
I take from one of my last series of observations.
On the 20th of June last, operating successively with two ther-
mometers, the spherical reservoirs of which had the diameters 12
millims. and 7 miDims. respectively, and with three different aper-
tures a, 6, c of the diaphragm, the respective diameters of which
were 17*5, 14*5, and 12 milluns., I obtained the following results : —
Time.
the enceinte.
Temperature of the
Temperature ctf the
•mall thermometer.
h m
240
255
3 10
3 30
3 45
4 10
4 SO
4 35
1410
14U6
1405
1400
13*95
13-90
13-85
13-30
2?03 (diaphragm a)
26-56 (diaphragm h)
24-05 (diaphragm h)
23-63 (diaphragm c)
23*85 (diaphragm a)
28-43 ((Saphraga a)
23-30 (diaphragm «)
28-05 (diaphragm a)
Let us take first the observations of 2* 55" and 3^ 10* ; these
two, made nearly at the same time, should lead to sensibly equal
excesses of temperature. The considerable difference between the
two numbers observed arises from the complication introduced into
the experiment by the presence of air ; to the radiation from the
bulb of the thermometer is added the cooling produced by the air ;
and in these two ways the bulb loses a quantity of heat equal to
that which it receives from the sun. The loss of heat in vacuo,
making equilibrium with the same quantity of heat received from
the sun, would therefore be equal to the loss observed plus the loss
due to the air. But, according to Bulong and Petit, the lowering
Digitized by VjOOQ IC
Intelligence and Miacellaneoue Articles. 235
of temperature resulting from this last cause can be represented by
g r>**^, m being a constant dependent only on the elasticity of the
air, and r the observed excess. We should have, then, in vacuo
with the two thermometers the two equal excesses
12-6H-^12-51»«»=10+^10>-233, whence w=2-24.
o 3-5
Let us take in the same way the observations of 3^ 45"^, 4^, and
4^ 20™, all three made with the same diaphragm, but different from
the preceding one; they conduct to the equation
9.77-1. ;^9-77»««»=12-15+ ^12-15>«», whence m=2-09.
3*5 0
Let us adopt for the value of the coefficient of cooling m the mean
of the two values thus obtained, ms=2'15 ; with the aid of this co-
efficient we can draw up the following Table of the temperatures
which would have been observed in vacuo : —
Time.
Temperature of
the enceinte.
Temperature of the
large thermometer.
Temperature of the
imall thermometer.
h m
2 40
2 55
3 10
330
3 45
4 0
4 20
4 35
1410
1405
14*05
14-00
13-95
1390
13-85
13*80
3l-40(dUphragma)
34-61 (diaphragm h)
34-54 (diaphragm »)
33*65 (diaphragm c}
34-20 (diaphragm a)
38 50 (diaphragm a)
33*10 (diaphragm a)
33^83 (diaphragm a)
On tracing the curve representing the course of the thermometer
for one and the same admission-aperture, it is readily recognized
that the relative temperatures at the different periods all combine
with perfect regularity, whether they come from the large or the
small thermometer.
Let us now consider two experiments made with different dia-
phragms ; and as the small thermometer is that which approximates
most nearly to the theoretical conditions (especiaUy for small ad-
mission-apertures), let us take the three experiments relative to
3^ 10", 3** 30", and 3** 45". Making use of the curve of the tem-
peratures for the diaphragm a, and reducing all to one and the
same temperature, 14°, of the enceinte, we have for the tempera-
tures at one and the same period: —
Diaphragm a 34*45
Diaphragm h 34-08
Diaphragm c 33*70
Applying to these data the equation I established in my previous
Digitized by VjOOQ IC
236 IiUelligenee and Miscellaneoui Articles.
note,
Sa«=Sa+*»a'+Oay or fl^— a'= ^0*+ -^ of,
we have
(Dii^h. a) l-0077»***-l-0077>*« igieo ^'^^^'^'
+ (0.0009493- ^g3^)l.0077..
(Diaph. 6.) l-0077»*w-l-0077"» jg^ 1-0077'
whence x=1355°, and
(Diaph. a) l-0077"«-l-0077'«= 1^60^'^^'^'^'
(Diaph. c) l-0077«-'-10077'«= Jg^o ^'^'^'^'
(0-0009493- ^^)10077»,
'*- 18^60 1-0077'
whence a? =1363°.
The agreement of the two values of x shows that the correction
necessitated by the radiation of the region of the sky in the vicinity
of the sun is made with sufficient exactness by writing for the total
radiation of the different portions of this surface ^ of, as if all
these parts were at one and the same mean temperature y.
Therefore, in the example selected, it will be concluded from these
calculations that, on the 20th June, at Grenoble, the temperature
of the sun, defined as I have indicated above, was, at 3^ 30'°,
1354°.
But this number itself, to give the true temperature of the sun,
ought to be further corrected on account of divers influences, par-
ticularly the absorption of the terrestrial atmosphere. It is chiefly
by operating at different altitudes, and (of course) noting the pres-
sure and the hygrometric state of the air at each station, that I
hope to solve this problem. For this purpose I have already made
several ascents of the Alps ; and I shall resume them as soon as
possible. — Comptes Bendus de TAcad. dt$ Sciences, June 29, 1874.
Digitized by VjOOQ IC
Intelligence and Miscellaneous Articles, 237
PHYSICS OF THB INTERNAL EARTH.
BY D. VAUGHAN.
In 1853 I first attempted to trace the consequences of subter-
ranean heat, bj taking into consideration some facts and principles
which seemed to l^ave received but little attention. The results of
my inquiries on the subject were given in a circular in 1854, in a
pamphlet in 1856, and in a paper which I sent to the British
Association in 1861, and of which an abstract is published in the
Eeports of the Sections, page 134. In that paper I endeavoured
to show that the terrestrial crust, if reposing on lava of a declining
temperature, would receive accessions of buoyant solid material,
chiefly on such points as extend deep into the fiery menstruum, and
that the consequent growth of internal mountains would be inter-
rupted only by the occasional movements of vast portions of this
light matter to positions much higher than those at which they were
first deposited. To the collisions of such rising masses against the
weaker parts of the earth's crust I ascribe eiurthquakes ; but the
theory affords a more satisfactory explanation for volcanic phe-
nomena.
Avalanches of siliceous rocks, ascending through buoyimcy from
deep subterranean peaks or depressions, would lead to important
results by conveying heat from a lower to a higher stratum of the
internal earth. Owing their solidity to pressure, such stony masses
would fuse during the ascent ; and, like our mountain-floods, would
erode channels which must for a long period direct them to the same
localities. The same spots of the earth's crust, being thus exposed
for many ages to the repeated inroads of intensely heated matter
from great depths, would be reduced in thickness by the frequent
fusion, and would present a weaker barrier to subterranean vio-
lence. Such an internal convection of heat would end in perforating
the earth's crust and producing an immense lake of lava on its sur-
face, were it not for the cooling influence of aqueous action ; and the
presence of water on our globe, though tending much to increase
the violence of earthquakes and volcanic eruptions, has the effect of
confining their ravages within a more limited range. To the
absence of water from the moon we may ascribe the enormous
diameters of the craters of lunar volcanoes ; while their height is
displayed on a far less scale, and there are no long ranges of lunar
mountains. On our satellite also volcanoes have for the most part
an insular character, conforming little to the linear arrangement so
common on the earth ; so that the cooling agency of water appears
to have been concerned in producing the vast rents or fissures on
which so many volcanic ormces seem to be located.
Apart from the evidence which the pendulum and geodetic mea-
surements give of inequalities on the invisible side of the earth's
crust, it can be proved theoretically that they are inevitable in the
course of solidification over the molten mass. One source of solid
matter light enough to form the external framework of our globe
Digitized by VjOOQ IC
238 Intelligence emd Miscellaneous Articles.
is to be found in the decomposition of many of the heavy silicates
by enormous pressure when the temperature of the menstruum in
which they were fused sunk below the melting-point of quartz.
An equivalent of oxide of lead and of crystallized silicic acid would
have their common volume increased about 14 per cent, on comlH'
ning and forming lead glass. Now, at a depth of 1000 kilometres
below the earth's surface, the pressure is equal to about 300,000
atmospheres ; and accordingly the formation of a cubic inch of
glass by the union of quartz and oxide of lead would, in conse-
quence of the expansion it involves, be resisted by a force the ther-
mal equivalent of which may be represented by the heat expended
in melting 14 cubic inches of ice. A force of equal energy would
be exerted by the same pressure for the decomposition of a cubic
inch of silicate of lead, in the supposed locality, and for the crys-
tallization of tiie resulting silicic acid. As far less heat is evolved by
the union of the strongest adds and bases, and as a crystallization
or atom-arrangement can make no heavy demands on force, it is
reasonable to conclude that in the supposed case chemical affinity
would be overruled and that the silicate ai lead would be decom-
posed. From similar estimates it would also appear that other
silicates, especially those of heavy metals, would undergo a similar
decomposition at great depths, and would part with their silica
when the temperature became low enough to allow its solidification.
Another source of buoyant matter is to be found in the transfer
of silica from the heavy metallic oxides to the alkalies and other
strong bases. The light compounds thus formed would, according
to Delesse and Deville, contract more than other igneous rocks in
passing into a solid state ; and it is evident that in propcnrtion to
this contraction vnll their production be favoured by pressure on the
decline of the primitive heat. The growth of a floatmg crust would
also be promoted by other circumstances. Of many of the metallic
oxides, the most infusible compounds are those in which the silicic
acid is very small or in a very large proportion. But the latter
bodies, which have almost invariably the lowest specific gravity,
bave also their fusibility reduced most by pressure m consequence
of the contraction which they undergo in assuming a solid form.
On this point more satisfactory evidence may be obtained by an
investigation similar to that of Clausius, but in which the effects of
pressure upon fusion is determined frcmi the change of volume and
the modulus of elasticity.
Of tJie various products which separate from the subterranean
lava in cooling, the most dense parts would sink to the centre,
though solidifying in the uppermost stratum ; while the li£;hter
material, though taking the solid form at great depths, would rise
towards the surface. But the solidity of the light silicated matter
could be permanmit only when kept under the influence of immense
pressure, by settling on prominent points which extend from the
inner side of the crust deep into the lava. The great centres of ac-
cumulation of this buoyant matter must be under continents, where
Digitized by VjOOQ IC
Intelligence and Miscellaneous Articles. 239
the eArtb's crust has evidentlj the greatest thickziess and reposes
on the deepest internal prominences ; and to the ocoasional slides
and asc^iding movements of matter from these parts ot the subter-
ranean regicMis, we may ascribe the prevalence oi vulcanicity on so
many continental coasts.
If only one per cent, of terrestrial matter passed into a solid form
in the course of ten miUicms of years, there would be still sufficient
grounds for assigning to rock-slides a mass so great that the me*
chanical effects of their collisioos against the thinner parts of the
crust mayproduce the most violent earthquake shocks. But the most
obvious efcecta must be ascribed to the sudden elevation of tempera-
ture which the thin spots of the earth's crust should experience,
and which may be reasonably estimated at many thousand degrees.
Exposed to such a fierce heat, the solid structure would be rent by
the unequal expansion of its parts, or by the elasticity of its volatile
constituents. 8team would manifest an irresistible power when
rock containing moisture tumbled into tlie molten liquid or encoun-
tered it wh^i penetrating through fissures. But a motive power
of long continuance would arise from the property which silica has
pf expelling other acids from bases at high temperature. As the si-
liceous rocks come into coUisicm with the strata containing limestone
or any other carbonates, the resulting mass should swell with the
evolution of carbonic acid, and boil over a volcanic crater or even
open a new (me. In consequence of the pressure, this expulsion of
carbonic acid will require a higher temperature ; and the cooling,
chiefly through the agency of water, would soon occasion a state of
repose until there occurred a new influx of heated matter from
deep regions. An estimate of the rate of cooling, as invdved in
the mere production of steam alone, would show that, during their
numerous eruptions, Etna and Vesuvius must have 1/ost a quantity
of heat too great to be supplied by any conceivable chemical or
mechanical action in their immediate vicinity ; and evidence may be
thus obtained of the necessity of the convection of caloric, and of
the introduction of incandescent matter from distant localities to
the theatre of volcanic activity.
CiDcinoati^ 0., July 16, 1874.
ON THE CONVERSION OF ORDINARY INTO AMORPHOUS PHOS-
PHORUS BY THE ACTION OF ELECTRICITY.
In the Anzeiger of the Imperial Academy at Vienna, Professor
V. Schrotter gives the following notice of this transformation, dis-
covered by Dr. Geissler : —
Already in 1860 Dr. Qeissler endeavoured to show that electri-
city by itself effects this change ; and he had the goodness, on the
occasion of his visit to Vienna at the time of the Universal Expo-
sition, to give up to me some of the glass apparatus.
The simplest of these is an exhausted glass tube of about 35 cen-
Digitized by VjOOQ IC
240 Intelligence and Miscellaneotu Articles*
tims. length and 2 centims. diameter, to the ends of which additions
were attached (by fusion) containing the conducting-wires, so that
in the experiment the wires were at least 45 centims. distant from
each other. The tube was filled with phosphorus vapour of very
little tension ; after the experiment its sides were coated with a
thin layer of amorphous phosphorus brownish red changing to
ffolden yellow, and in many places exhibiting the colours of thin
films.
The second apparatus serving for the same purpose, a master-
piece of the glassblower's art, has the form and sue of a beaker-
shaped double-walled champagne-glass. The thin layer of amor-
phous phosphorus distributed over the inner surfaces of its walls
exhibits the play of all the colours of thin films, giving to the glass
a pleasing appearance.
The third, still more elaborately executed apparatus is designed
to show that the conversion of the phosphorus is effected even by
the inducing action of the current. For this purpose the ends of
the two aluminium conductin^-wires are inserted in exhausted
spheres in which there is no phosphorus. These spheres are en-
closed in others, which are united by a tube 40 millims. long and 1
millim. wide. The interspaces thus formed, likewise exhausted,
contain the phosphorus, which is therefore completely shut off from
the conducting-wires by a wall of glass. The distance between the
conducting-wires amounts to 26, and the diameter of the outer
spheres to 5 centims. The interval between the walls of the
spheres amounts to 5 millims. Here also the inner side of the
outer, and the outer side of the inner sphere, in like manner as
above stated, were coated with amorphous phosphorus. Only in
the narrow connexions was no phosphorus deposited.
The above-mentioned facts furnish, perhaps, the best demonstra-
tion that the conversion of phosphorus into the amorphous modifi-
cation is effected neither by the light nor by the heat which accom-
pany the current, but exclusively by the electricity itself.
The instructive experiments which Hittorf published in 1865
(Pogg. Ann. vol. cxxvi. p. 195) were made with another arrange-
ment of the apparatus, as the platinum wires, fused into glass
spheres of 6 to 8 centims. diameter, were only a few millims. dis-
tant from one another ; so that sparks passed, and the course of
the phenomenon was somewhat different from that above described ;
but the conclusions deduced therefrom by Bittorf were the same.
I hope to be able to resume this subject in greater detail ; for
the present the above account may suffice to recall attention to it.
— Poggendorff's Annalen^ vol. clii. pp. 171-173.
Digitized by VjOOQ IC
THE
LONDON, EDINBURGH, and DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE-
[FOURTH SERIES,]
OCTOBER 1874.
XXXIV • On Gladstone's Experiments relating to Chemical Mass.
By Edmund J. Mills, D.Sc, F.R.S*
I. rpHE Philosopbical Transactions for 1855 (vol. cxlv.) con-
J- tains an important memoir by Gladstone " On Cirenm-
stances modifying the Action of Chemical Affinity/' In this
memoir numerous sets of experiments are described, which
mainly serve to determine, by means of an increase or diminu-
tion of colour, the progress of certain selected reactions. The
results are exhibited in curves, several of which show a regular
course, while all are continuous ; but no mathematical expres-
sion of the law of action^ is given. About eleven years after-
wards (Phil. Trans. 1865-6) it was shown by Esson, on the
basis of Harcourt's experiments, that when a substance under-
goes chemical change, the residue y of changing substance is
connected with the unit intervals x of change (time, reagent, or
other operator) by the equation
where a represents the amount of substance originally present,
and « the amount of it disappearing ])er unit o(x. This relation
is graphically represented as a logarithmic curve ; but, as a rule,
even in very simple cases, its expression is more complex, and
corresponds to the form
which indicates that two bodies are undergoing change, or that
one body is undergoing dual change. In cither case the amount
♦ Communicated by the Author.
Phil. Mag. S. 4. Vol. 48. No. 318. Oct. 1874. R
Digitized by VjOOQ IC
242 Dr. E. J. Mills on Gladstone's Experiments
of change per unit interval is proportional to the amount of sub-
stance then changing.
As Gladstone's results were the first in which the continuity
of the chemical process was experimentally demonstrated (at any
rate on a sufficient scale)^ I felt much interested in ascertaining
whether Esson's equation would apply to them^-especially when
I considered how few have been the contributions to chemical
dynamics^ the laborious (and consequently unpopular) nature of
such researcheSi and the inexpediency of allowing good work to
remain dumb or unexpressed.
II. The colorimetrical method^ which was used throughout by
Gladstone, has considerable disadvantages, and is most service-
able when only small quantities, as in the case of the Nessler
test, have to be measured and an inaccuracy of about 5 per cent,
is of no consequence. It is probable that the observer's estimate
of colour varies during a long course of experiments, and is
really under training in the earlier ones; so that, as will
actually be found below, all the more serious errors occur, as a
rule, at the outset. We must also remember that colour-effects
in solutions are not unfrequently slow in attaining their maxi-
mum, thus making a particular observation too low; on the
other hand, the subsequent arrival of this maximum will make
a following observation too high : hence also, by virtue of com-
pensation, the later observations may be expected to be mora
correct.
A further difficulty lies in the computation itself. The amount
of chemical energy (or substance) originally present is not given
in terms of the reagent, and has to be arrived at by successive
and wearisome approximations; and these might perhaps have
been carried a stage further with advantage. Again, the sue-
cessive values of a are very seldom given in the experiments,
which had not been arranged to test any particular hypothesis;
they had consequently to be obtained by graphic interpolation
on curves which, for such a purpose, should have been consider*
ably longer.
If we bear in mind these and other drawbacks, we shall regard
the coincidence between theory and experiment as very striking.
III. Ferric Nitrate and Potassic Sulphoct/anide [loc. cii. p. 187,
pi. 7. fig. 1). — ^To one *' equivalent '' of ferric nitrate successive
groups of '^ equivalents '' of potassic sulphocyanide are added,
in presence of water; the amount of "red salt produced*^ is
estimated by eye-observations, the liquid being diluted for that
purpose up to a standard. The total amount a of red salt thus
producible represents in special measure the original unexhausted
energy of the nitrate. I have taken each unit of x as represent-
ing 25 '' equivalents " of potassic sulphocyanide. The equation
Digitized by VjOOQ IC
relating to C/iemical Mass.
243
19
y=401(-8550)'+224(-1516)';
bat the results are expressed in percentages of the initial value
ofy.
Tablb I.
a.
y, calculated.
jff found.
1
60-3
60-2
2
477
477
3
40-2
39-2
4
34*3
330
5
29-3
28-5
6
251
24-5
7
21-4
20-6
8
183
178
9
15-7
15-4
10
13-4
13-3
11
11-5
117
13
9-8
10-4
13
8-4
8-8
14
71
7-2
15
61
61
Gladstone gives two variations of this experiment.
IV. Ferric Sulphate and Potassic Sulphocyanide {loc. cU.
p. 189, pi. 7. fig. 1). — On accouut of the weakness of the colour
produced when a sulphate is present, the amount of the salts
employed was doubled. One equivalent of ferric nitrate was
taken. The equation is
y=488 {-8208)'+ 182 (-1400)';
and the unit of x is 15 equivalents.
Table II.
X.
y, calculated.
y, found.
1
66-3
653
2
b2'2
53-9
3
42-6
44-2
4
34*9
35-6
5
28-6
287
6
23-5
237
7
19-3
19-6
8
15-8
15*3
9
13-0
12-0
10
10-7
96
11
87
81
12
7-2
6-7
13
5-9
5-6
R2
Digitized by VjOOQIC
244 Dr. E. J. Mills an Gladstone's Experimenti
V. Ferric Chloride and Potctmc Sulphocyanide (loc. ^ii. p. 189,
pi. 7. fig. 1). — ^This experiment is described as "precisely ana-
logous to the preceding.^' The equation is
y=406 (•8900)'+214 (-2500)';
and the unit of x is 20 equiyalents.
Table IIL
4r.
y, calcnltted.
y, found.
66-9
65*0
54H)
34-0
467
46-9
41 •«
41-9
36-6
36-8
39*6
83-9
99-0
99-5
95-8
95*8
99-9
99-9
10
90-4
900
11
18-9
173
19
169
14-8
VI. Ferric Nitrate and Hydric Sulphocyanide {loc. cit. p. 190,
pi. 8. fig. 2). — ^Ferric nitrate, 1 equivalent. Unit of ^ = 4 equi*
Talents. The equation is
y=533B (-91093)' +89-5 (-82670)'.
Table IV.
4*.
y, ctlculaied.
y» found.
1
89-7
897
9
72-6
731
3
653
65-3
4
59 1
58*9
5
538
53-9
G
49^
496
7
446
45-3
8
406
413
9
370
37^
10
• 337
34-4
11
30 7
319
The above results seem to have been the sequel of consider-
able experience with the method, and are in exceptional ac-
cordance with theory.
VII. Ferric Citrate and Hydric Gallate {loc. cit. p. 193, pi. 9.
fig. 1). — One equivalent of ferric citrate was mixed with 6 kc
equivalents of hydric gallate, and the increasing black coloration
measured. Unit of or = 3 equivalents. The equation is
y=660 (•9127)'+90 (•8072)'.
Digitized by VjOOQ IC
relating to Chemical Mass.
Table V.
245
4r.
y, calcnlated.
y, found.
1
840
867
2
74-4
•76 0
3
G72
68-4
4
612
621
5
65-8
56-3
6
50-9
50-8
7
464
460.
8
42-4
41-7
9
38-7
380
10
85-3
347
11
322
321
VIII. Ferric Citrate and Potassic Ferrocyanide {loc. cit. p. 199,
pi. 9, fig. 5). — One equivalent of ferric citrate was mixed with 3
&c. equivalents of potassic ferrocyanide in presence of bydric
oxalate, and the increasing blue coloration determined. Unit
of ;r s 3 equivalents. The equation is
y=102 (•2010)'+23 (-7699)'.
Table VI.
X,
y, calculated.
y, found.
30-6
29-6
142
11-4
91
9-8
66
6-4
50
4-0
IX. The above equations represent the greater part of Glad-
stone's results as figured at the end of his memoir. I have not
worked out the remainder, either (1) because they form mere
continuations or repetitions of the reduced curves, or (2) because
the experiments were not numerous enough, nor the theory of
the reactions sufficiently evident, to enable the calculation to be
made. The curves representing the formation of ferric meco-
nate and acetate somewhat resemble, but are not identical with,
the cubical parabola. Similar ones are drawn by Harcourt and
Esson (Phil. Trans. 1866, pi. 17), and Guldberg and Waage
{Etudes sur les Affinit(s chimiques, Christiania, 1867, pis. 14, 15,
16). It is obvious that they represent duplex reactions ; but
their complete reduction may perhaps be a matter of consider-
able difficulty.
In order to estimate the accuracy of the experimental work,
and the soundness of the hypothesis involved in its symbolic
^xpressioi)^ I have drawn up the following en*or Table, showing
Digitized by VjOOQ IC
246 On Gladstone's Experiments relating to Chemical Mass.
a sammary of the differences between calcolation and observation^
as compared in percentages.
Table VII.
AboTe S-3.
Above 1-S
(inclusive).
Above 0-5-1-0
(inclusive).
Above 0HM)-5
(inclusive).
Table I
Table II. ...
Table III. ...
Table IV. ...
Table V. ...
Table VI. ...
0
0
0
0
I
0
I
3
2
0
9
0
0
6
8
6
4
8
Total!
1
8
2S
86
The entire number of comparisons is sixty-seven. Thus it
appears that 64 per cent, of the errors are such as would^ on
their average^ be found in very good analytical work ; 33 per
cent, of them occur, on their average, in ordinarily good analy-
tical work ; the remaining 13 per cent, lie, on their average,
within the usual limits allowable in colorimetry,
X. The foregoing equations show that any such expression as
i[Fe«Cl«] + 3KpNS=i[Fe*(CNS)«] + 3KCI
h wholly erroneous^ if intended to represent the chemical energy
of a ferric salt, or the amount of potassic sulphocyanide that is
capable of acting thereon; for the energy of the quantity
i[Fe«Cl^ is not exhausted until about 400 units (KCNS) have
been brought to bear upon it ; and other ferric salts are repre-
sented by similarly high numbers. The ordinary equations of
chemistry represent the result of distributing weight, and give
no account of work done ; these, on the other hand, represent »
dynamical process as well as distribution of weight. Hence it is
clear that the '^equivalents^' or valencies inferred from the com-
mon equations rest upon a wholly fallacious basis, and cannot
be depended upon in scientific reasoning. To assert, for instance,
that G is equivalent to U^, amounts to stating that hydrogen
and carbon have been compared as to the work they can do
under certain circumstances, just as ferric chloride is compared
with ferric sulphate in Gladstone's experiments. No such re-
search has, however, been made ; and it would not be likely to
Q
yield the ratio TTi =1 i^ it were made. What, then, becomes of
the doctrine that carbon is tetravalent ?
It is worthy of remark that, while the ordinary equations in-
variably express that quantity consists of parts (that, for example^
potassic chloride contains potassium and chlorine, whereas we
Digitized by VjOOQ IC
On a very singular Sulphuretted Nitroffenoue Confound. 247
only know that it contains the joint weights of potassium and
chlorine)^ the logarithmic equations make no suggestion upon
this subject. All the above experiments might have been accu-
rately performed and symbolically expressed by a person totally
ignorant of the ''constitution'* of ferric salts or of potassic sul-
ptioeyanide ; and the reagent might have been extremely impure,
provided that it produced a red coloration. What we owe to
Esson and Gladstone we might have inherited from Wenzel or
Cavendish,
12 Pemberton Terrace,
8t. John's Park. N.
XXXV. On a very singular Sulphuretted Nitrogenous Compound,
obtained by the Action of Sulphide of Ammonium on the Hydrate
of Chloral. By Edmcnd W. Davy, A.M., M.D., M.R.I, A.,
Professor of Forensic Medicine, Royal College of Surgeons,
Ireland, and late Professor of Agricultural Chemistry, Royal
Dublin Society^.
THE substance termed hydrate of chloral, or chloral hydrate,
from the many valuable therapeutic properties it has re*
oently been found to possess, has within the last four or five
years been prepared in considerable quantities, and has become
an article of some commercial importance; and numerous as
are the useful applications which have already been made of
that substance in medicine, there can be but little doubt that
their number may be greatly increased; so that we may justly
regard chloral hydrate as one of the most, if not the most, im-
portant of the recent additions to our materia medica.
It being thus a substance of such practical importance, any
information which may tend to extend our knowledge of its che-
mical properties and relations should not, I conceive, be regarded
as devoid of interest. I shall therefore briefly state the results
of some observations which I have recently made as to the action
of sulphide of ammonium on that substance (a subject that has
been but little studied), and describe the properties of a very
singular compound thereby produced, the constitution of which,
as far as I am aware, has not hitherto been determined.
When sulphide of ammonium is added to an aqueous solution
of chbral hydrate, the mixture after a few moments acquires a
deep yellow colour, and, rapidly becoming orange, passes to
a reddish brown, which finally assumes so dark an appearance
that the liquid, when in any quantitv, looks almost black by
reflected light. It was also observed, after the mixture had
* Communicated by the Author.
Digitized by VjOOQ IC
248 [Dr. E. W, Davy on a very singular
assumed an orange tint, that almost immediately more or less
of a solid matter invariably separated from the liquid^ appear-
ing at first of a bright orange or light red colour, from its being
suspended in the orange or red liquid, but that, after it was
separated from it by filtration and washing, it was found to
possess a light brown appearance. Whilst the changes just de-
scribed were taking place, it was also noticed that the mixture
became sensibly warm to the hand, and that the odour of the
sulphide disappeared, whilst that of ammonia and of chloroform
was easily detected.
It was further ascertained that when the dark reddish-brown
liquid obtained in the way just stated was acidified with an acid,
it yielded a copious brown precipitate, which, though somewhat
darker in its colour than that which separates from the liquid
before the addition of the acid, appears to be essentially the
same compound, the difference of shade being probably due, at
least in some measure, to different amounts of free sulphur
present in each.
As the principal feature of interest connected with the reac-
tion referred to, I considered, was attached to the formation
of the brown solid compound just noticed, a quantity of it
was made as follows : — Four hundred grains of chloral hydrate
being dissolved in about ten ounces of distilled water, sulphu-
retted hydrogen was passed through the solution till it poss^sed,
after being shaken, the odour of that gas. Sulphide of ammo-
nium was then added in small portions at a time, continuing
the passage of the sulphuretted hydrogen through the mixture
when the effects before described were produced. This treat-
ment was continued till no further action appeared to take place,
and the mixture possessed, after being well shaken, a strong
odour of sulphuretted hydrogen.
I ma^ here observe that, after the addition of the sulphide of
ammonium, the evolution of ammonia was from the first percep-
tible, whilst the odour of the sulphide and of the gas for some
time continually disappeared, and it was not till the later stages
of the process that the smell of chloroform could be detected.
To the mixture so treated, which was distinctly alkaline, pure
diluted sulphuric acid was added till it acquired an acid reaction,
and the whole was thrown on a filter, when the brown solid was
separated from a deep amber-coloUr^d liquid. The former was
then washed with cold distilled water till no indication of sul-
phuric acid in the filtrate could be detected by chloride of barium;
but finding that it exhibited traces of ammonia when treated with
caustic lime, the washing of the brown solid was continued, first
using cold distilled water ; and this failing to accomplish the
object sought, it was washed with a considerable quantity of hot
Digitized by VjOOQ IC
Sulphuretted Nitrogenous Compound. 249
distilled water till the presence of ammonia could no longer be
discovered in the filtrate. The brown matter was subsequently
dried, first by exposure to the air on the filter at the ordinaiy
temperature^ then at a very gentle heat^ and afterwards by ex-
posing it for some time under a bell-glass to the drying influ-
ence of sulphuric acid.
As I thought it more than probable that the substance, from
the way in which it had been procured, contained some free
sulphur (which was afterwards shown to be the case), a portion
of that which had been so dried was placed in a stoppered bottle
and digested for some days along with bisulphide of carbon ; the
mixture was then thrown on a filter, and washed with repeated
fresh portions of pure bisulphide till but a faint trace of residue
remained after the evaporation of a little of the filtrate; and this
seemed to be due, not to sulphur as at the first, but to the brown
compound being soluble to a very slight degree in the bisul-
phide. After this treatment the bisulphide was allowed to eva-
porate off from the substance, when it was placed as before under
a bell-glass along with a vessel containing sulphuric acid, where
it remained for some days. Thinking, however, that it might
still not be perfectly dry, it was subsequently heated in a water-
bath or oven to about 212° F., when I found that a very slight
amount of moisture was expelled from it, accompanied by a pe-
culiar sulphurous smell ; and as soon as it appeared to lose no
further weight by this temperature, it was placed in a well-stop-
pered bottle and reserved for examination.
The substance so obtained, and in this dry condition, possesses
the following properties: it is an amorphous solid of a light
brown earthy appearance, is easily reducible to a state of impal-
pable powder, and has a specific gravity of about 1*62. When
gently heated on platinum-foil it evolves a very peculiar odour,
then blackens, partially fuses, and, taking fire, burns with a pur-
plish-coloured flame, emitting a faint odour of sulphurous acid,
whilst it leaves a large carbonaceous residue, which on the appli-
cation of a stronger heat ignites and slowly burns away.
It is very slightly soluble in water, alcohol, bisulphide of car-
bon, and in ether , whilst it is almost insoluble in chloroform
and in benzol. It is, however, readily dissolved by solutions of
the caustic alkalies, and by those of the alkaline cai*bonates and
sulphides, forming dark brown or reddish-brown solutions, from
which it is again precipitated, apparently unchanged, by the ad-
dition of an acid in excess. It dissolves also in solutions of the
hydrate of lime and of baryta, and is soluble to some extent in
alkaline chlorides and iodides.
As to the action of acids, when it was treated with concen-
trated sulphuric acid it acquired a darker colour, and dissolved.
Digitized by VjOOQ IC
260 On a very iingular Sutphweiied Nitrogtnow Compound.
forming a brown tolution^ which on being heated became almost
black in appearance ; and this on the addition of water gave a
flocculent dark brown precipitate resembling the original sab*
stance^ except in its being of a darker colour.
Strong nitric acid^ even at the ordinary temperature^ was
found to act rapidly on the substance^ which it oxidises and disi
solves; but neither it nor sulphuric acid in a diluted condition
appears to exercise any effect on it \ for when boiled for some
time with them no apparent change was observed to take place.
As to hydrochloric acid^ even when in a tolerably concentrated
condition it seemed not to produce any effect on the substanee
either at the ordinary temperature or when boiled with it.
The compound^ some of the properties of which have just been
noticed^ on being submitted to analysis gave results which agree
most closely with the formula C"» H«* S*' N* 0®, showing that
the substance is an extremely complex one^ the formation of
which> under the circumstances described^ may be explained by
supposing the following reaction to take place : —
9(C«HC1«0,H«0) + 16[(NHVS]+2H«S=C«H«*S«N^0«
-f"27(NH*Cl)-f"NH»+5S + 12H«0,
where 0 equivalents of chloral hydrate^ being acted on by the
conjoint action of 16 of sulphide of ammonium and 2 of hydro-
sulphuric acid; give rise to the formation of I equivalent of the
brown compound^ together with 27 of chloride of ammonium^
1 of ammonia^ 5 of sulphur, and 12 of water^ 9 of which latter
exist already as constituents of the chloral hydrate; and the pro-
bability that such changes do take place appears to be strength-
ened by the fact that chloride of ammonium^ ammonia, and free
sulphur were detected amongst the products of the reaction ; and
the presence of a trace of chloroform may be easily accounted
for by the action of the free ammonia on a portion of the un-
changed chloral hydrate.
I may observe that those results as to the composition of the
brown compound were obtained as follows : — The carbon and
hydrogen were determined by combustion with chromate of lead,
using a long combustion-tube and placing a layer of copper
turnings in its anterior part ; the nitrogen by burning with
soda-lime, and estimating the resulting ammonia by means of the
chloride of platinum; the sulphur by converting it into sul-
phuric acid, which was effected by treating the substance with
nitric acid and chlorate of potash (as recommended lately by
Pearson for the determination of sulphur in organic compounds),
and then estimating the sulphuric acid so pi*oduced in the usual
way by chloride of barium ; and lastly the oxygen was deter-
mined by difference after the estimation of the other constituents.
Digitized by VjOOQ IC
Dr. A. SchuBter on Unilateral Conductivity. 361
But I may remark that the peculiar properties and great com-
plexity of this compound offer considerable difficulties in the
way of an exact determination of its different constituents^ and
of its true nature as a chemical combination. It appears^ how*
ever^ from the circumstance that it readily dissolves in alkaline
solutions^ which then yield insoluble or sparingly soluble dark-
coloured precipitates with different metallic salts, that it partakes
somewhat of the character of an acid ; but this and several other
obvious matters of inquiry connected with the compound are
subjects for further investigation.
Before concluding, it is right to state that, after I had observed
many of the facts which I have here described, I found, on look-
ing over the ' Chemical News/ that there was in volume xxv.
page 87, a notice of a communication *' On the Reaction of
Chloral Hydrate and Sulphide of Ammonium,'' which had been
read by Dr. J. Wala before the Lyceum of Natural History of
New York, in which he notices some of the changes which I
have described as taking place in that reaction, as well as the
formation of a light-yellow substance, the properties of which
(as observed by him) do not altogether agree with those of the
sulphuretted compound, which I prepared in a somewhat differ-
ent manner from that which he adopted. I may also add that
Dr. Wah did not attempt to analyze the substance he obtained,
for want, as he says, of material — and that he further states, in
speaking of it, that 0. Low asserts that in physical appearance
and chemical properties it resembles exactly the sesquisulphide
of carbon which he has described in the American Journal of
Science, vol. xli. p. 251.
Be this as it may as regards the substance obtained by Dr.
Walz, my analyses of the brown sulphuretted compound, pre-
pared in the manner stated, show that it possesses a totally dif-
ferent chemical composition from the sulphide described by L5w
in the Journal to which he has referred.
XXXVI. On Unilateral Conductivity.
By Arthur Schuster, Ph>D.^
I. Introductory,
WHILE I was engaged in other work I met with an irre-
gularity which seemed to me to be of such a peculiar
nature that I subjected it to a separate investigation. The
residts of this investigat'on have not been entirely satisfactory.
I have not been able to raise the phenomenon, to which I allude,
* Commimicated by the Author, having been read in Section A. of the
British Association at Belfast (1874).
Digitized by VjOOQ IC
253 Dr. A. Schuster on Unilateral Conductivity*
above the rank of an irregularity ; that is to 8ay> I am not able
to produce it at my own will^ although when it is present I am
generally able to destroy it. My experiments, however^ leave
no doubt as to the facts^ and they show clearly that^ in a circuit
composed entirely of copper wires, joined together by means of
binding-screws^ the electric conductivity may be different in
opposite directions. It would be difficult to discover such a
difference in the resistance by means of the ordinary ways of
measuring it. The changes in the electromotive force of the
battery and in the resistance of the wire^ through an alteration
of temperature or other accidental causes^ would be sufficient to
mask the effect. If we use, however, the electromotive force of
a moving magnet, we are sure that it is always constant as long
as the strength of the magnet does not vary and the magnet
moves always between certain limits. A magnet rotating rapidly
within a coil of wires induces currents in alternate directions in
the coil. We are perfectly sure that the electromotive force
producing these currents is the same in both directions ; and if
we can detect any difference in the strength of the currents
going in opposite directions through the wire, we may be sure
that only a difference in the resistance can produce such a result.
I have calculated the effect on the galvanometer-needle of in-
duction-shocks following each other in alternate directions at
regular intervals of time. If the galvanometer is provided with
a damping arrangement, a final condition will be arrived at in
which the galvanometer-needle swings between certain limits.
These limits decrease as the interval between the induction-
shocks decreases. If, therefore, the rotation of the magnet is
rapid enough, the effect of the induced currents on the gidvano-
meter ceases to be visible. It should, however, be remembered
that, although the limits between which the galvanometer-needle
moves approach zero, the velocity of the needle remains finite.
This, of course, is only true if the two induction-shocks are of
equal strength. If the induction-cuiTcnt in one direction is
stronger than the current in the opposite direction, the galvano-
meter will show a permanent deflection. As we have two strong
currents balancing each other, a very small difference in the
resistance will have a strong effect.
II. Description of Apparatus.
The magnet which was used as electromotive force was fixed
to the plate of a siren, which could be set into motion by means
of a pair of bellows. The same instrument has been formerly
used by R. Kohlrausch and W. Weber*, and later by Kohl-
* " Electrodynamic Measurements, with special reference to the reduc-
tion of intensitv to absolute measure,*' proc. pf the Royal Saxonian Society
of Sciences, vol. iii.
Digitized by VjOOQ IC
Dr. A. Schuster on Unilateral Conductivity. 233
rausch and Nippoldt iu a research on the conductivity of sulphuric
acid*. I take the following data from the latter paper. The
resistance of the wire wound round the magnet is 30 mercury
unitsf. The mean electromotive force of the induction-shocks is
-^-T Grove in each direction if the magnet rotates n times in a
second. During the following investigation the magnet rotated
about forty times a second ; so that the resultant electromotive
force in each direction was about 0*12 Grove.
The resistance of the galvanometer was found to be about
2477 mercury units ; so that the resistance of the whole circuit
was as nearly as possible 2500 units. The galvanometer had a
plane mirror, and was read off by means of a telescope and scale
at a distance. In order to have an idea of the delicacy of the
instrument, I measured the deflection produced by a known
electromotive force, and I found that the electromotive force of
TsVir Daniell caused a first deflection of 200*4 divisions of the
scale. The whole arrangement is therefore extremely simple,
and is represented by the following diagram :-^
© <$>
G is the galvanometer, I a coil of wires within which the rota-
ting magnet is placed.
III. Description of Experiments.
When I first joined the galvanometer to the inductor and ro-
tated the magnet, the effect on the galvanometer-needle was such
that I was afraid of a bad contact either in the galvanometer or
in the inductor. The needle started wild to one side, then
suddenly stopped, turned back to the opposite side, and moved
from one side to another without any law. The only regularity
I could perceive was that it started always in the same direction.
On changing the wires leading to the galvanometer, the needle
invariably started to the opposite direction. I broke the con-
nexions and left for about two hours. When I came back every
thing had changed. On working the siren the needle now went
slowly to one side, and after a few oscillations came to rest at a
point about ninety divisions of the scale from the zero-point.
On changing the wires leading to the galvanometer the needle
* " On the Validity of Ohm's law for electrolvtes, and a numeric deter-
mination of the conductivity of sulphuric acid. Poffff. Ann, vol. cxxxviii.
p. 379 (1869).
t All resistances in this research are referred to mercury units.
Digitized by VjOOQ IC
254 Dr. A. Schuster on Unilateral Conductivity.
went to the other side, and the permanent deflection was nume-
rically the same* The same experiment was repeated several
times, and the same deflection was always observed. While
thinking over this result, I took the apparatus to pieces, t. ««
disconnected all wires and joined them again together. The
effect had now entirely disappeared, the needle coming to rest
exactly at its sero-point* The next dav a small unilateral con-
ductivity (as the raect may be properly called) was observed,
but after a few experiments disappeared again. During several
days I found that this unilateral conductivity generally appeared
when the wires had had some rest ; and I therefore joined into
the circuit different wires which had not been used for some
time. Some of these wires showed the effect, and some did not ;
in all cases it disappeared after several experiments. A wire
which had never been used before showed the effect in a remark-
able degree. The introduction of this wire, which could not
have a resistance larger than 0*1 unit, was sufficient to drive
the needle wild to one side. I must mention here a remarkable
fact. Suppose we have a circuit in its normal state (that is,
showing no unilateral conductivity) ; let us introduce a wire, and
suppose that the unilateral conductivity is now observed. Take
the wire out again, so that the circuit is exactly the same as it
was before when no unilateral conductivity existed. The uni-
lateral conductivity will now appear, generally even in the same
degree as it did with the new wire. If we now by experimenting
destroy the unilateral conductivity and join the wire which had
caused the disturbance into the circuit again, it will generally
behave quite neutral ; t. e, no unilateral conductivity wUl be ob-
served. If it do not behave quite neutral, it will only show a
small unilateral conductivity, which will be destroyed by a second
or third experiment of the same kind.
IV. Proposed Theory of the Phenomenon.
It is chiefly the remarkable fact just described (as well as the
previous observation, that generally new wires, or such wires as
have not been used for some time, showed the effect) that has
led me to a theory which, although proved afterwards to be, if
not erroneous, at any rate incomplete, explains so well many of
the most startling observations that I think it welt to give it
here. Supposing we pass an electric spark from a sphere to a
point, it is known that the distance the electric spark will pass
for a given electromotive force is different according as the sphere
is positively or negatively electrified. A circuit composed of a
metallic wire, terminated at one end by a sphere, separated by a
thin layer of air from the other end of the wire would therefore
show unilateral conductivity, the positive electricity passing more
Digitized by VjOOQ IC
Dr. A. Schuster on Unilateral Conductivity. 255
easy in one direction through the air than in the other. It is
also known that metals condense air in great quantity at their
surface ; and if we screw two wires with their condensed air to*
gether, it is quite conceivable that particles of air will separate
the two surfaces of copper^ and that a small voltaic arc will there-
fore be formed. Unilateral conductivity would be the result.
If we screw a wire which has air condensed on its surface to a
binding-screw^ part of the air will pass from the wire to the
binding-screw ; and it would thus be explained that the tempo*
rary addition of a new wire may produce a unilateral conductivity
in a circuit which has not shown it before,
V. Experiments confirming the Theory.
Many minor coincidences seemed to confirm this theory*
Cleaning the ends of the wire with the knife generally destroyed
the effect. It was, as a rule, observed in those parts of the cir-
cuit which had been disconnected over night. It is always easy
to find out in what part of the circuit the effect has its seat.
We have only to change the connexions in various places, and
to observe in what direction the needle is deflected. I mention
one particular case.
The rotation of the magnet one day caused a permanent de-
flection of the needle of 295 divisions of the scale. On reversing
the wires at the ends of the induction-coil, the needle was de-
flected towards the other side. The effect, therefore, had its
seat in the induction-coil. The coil was divided into two halves,
which were connected by means of a stout copper wire about
half an inch in length. I remembered that this piece of wire
had been exposed to the air over night, and I therefore reversed
the wire ; the needle was deflected 295 divisions of the scale to
the other side, showing that my supposition had been correct,
and that this small piece of wire, the resistance of which may
have been about the hundred-thousandth part of the whole
resistance, had caused the deflection. On reversing the wire
again, the effect had disappeared.
Another wire was now taken to join the two halves of the in-
duction-coil ; a permanent deflection of about 80 divisions of
the scale was observed. On cleaning the ends of the wire with
a knife the effect disappeared.
These experiments seemed alone sufficient to prove the theory.
In order, however, to subject it to a severer test, I thought of
condensing air artificially on the surface of the wire. This can
readily be done by means of powdered charcoal, which, as is
known, absorbs air in great quantity. A wire which was in its
normal state was therefore laid with one end into powdered
charcoal for about five minutes. When reintroduced into the
Digitized by VjOOQ IC
256 Dr. A. Schuster on Unilateral Conductivity.
circuit, the wire showed a very strong unilateral conductivity.
Cleaning and scraping the wire had at first apparently no effect ;
screwing the wire^ however, to another binding-screw attached
to the induction-coil destroyed the effect entirely, so that the
wire, even when screwed to the original binding-screw, showed
no unilateral conductivity. The same experiment was repeated
a second time, and with the same result. Five minutes' lying
in powdered charcoal was sufficient to reproduce a strong
unilateral conductivity; and the same operation as before
destroyed it.
VI. Failure of the Theory.
A third trial to obtain unilateral conductivity by the same
means failed. The wire was put into the charcoal for several
hours instead of several minutes ; but even then it remained in
its neutral state. All the various circumstances which generally
had produced unilateral conductivity were now tried; but none
succeeded. New wires were tried; the whole apparatus was
left untouched and disconnected for several days ; but I could
not obtain the effect again. I used the same instrument in
another investigation during three consecutive weeks, during
which various new wires were tried and new combinations em-
ployed ; but the effect only came out once more, and this time
m the galvanometer. The deflection amounted to about 20
divisions of the scale. It lasted for several days and then dis-
appeared.
VII. Relation of unilateral conductivity to previously known
phenomena.
It is perhaps worth while to ^ay a few words about the rela-
tion in which the phenomenon described in these pages stands'
to other phenomena to which a similar name has sometimes been
given. Before attempting to do this, however, it is necessary
to allude to one or two objections which might be raised against
my interpretation of the experiments described above.
Can the experiments be explained by thermoelectric currents
set up by the heating of the wire through the electric vibra-
tions f I think that a careful perusal of the experiments will
convince everybody that they cannot be explained that way. I
need only draw attention to the unstableness of the effects and
to the different facts upon which I thought myself justified in
founding the theory mentioned above. These facts certainly
cannot be explained by thermoelectric currents.
At first sight my experiments seem to have some relation to
a class of phenomena discovered by Poggendorff*^, and described
♦ Annalen, vol. xlv. p. 353 (1838), vol. liv. p. 192 (1841).
Digitized by VjOOQ IC
Dr. A. Schuster on Unilateral Conductivity. 257
by him under the name of bilateral deflection {doppelsinnige
Ablenkunff), It seems that the currents in alternate direction
affect to a certain degree the temporary magnetization of the
needle. This has of course an influence on the time of vibra-*
tion, which is shorter while the current increasing the mag*
netism passes through the galvanometer. While the current
passes in this direction the needle makes a greater way than in
the same time while the current in the opposite direction is
passing. The two currents succeeding each other at regular
mtenrals of time will therefore not counterbalance each other^
but the current increasing the magnetism of the needle will have
the upper hand.
The result will be that the needle will be driven towards the
side to which it was originally deflected. This^ of course^ only
happens if the effect of this magnetization is sufficiently strong
— that is to say^ if the original deflection is sufficiently large ;
for the magnetizing effect on a needle^ placed at right angles to
the axis of the galvanometer-coil^ is zero^ and increases as the
sine of the angle of deflection. According to Poggendorff,
a needle which is not deflected more than eight or ten degrees
from its zero-pointy will return to that point if currents in alter-
nate directions are sent through the galvanometer. If, how-
ever^ the original deflection is greater than 10 degrees, the
needle is driven violently towards the side of this deflection.
It is evident that this effect of the electric vibrations is a
function merely of the position of the needle ; altering the con-
nexions could therefore never produce a reversal of the effect.
As, however, I could always drive the needle towards the other
side by suitably changing the connexions, this bilateral deflec-
tion has evidently had nothing to do with the abpve experi-
ments.
It remains to say a few words about what has been called
unipolar conductivity. This unipolar conductivity has been ob-
served in electrolysis and in flames. The unipolar conductivity
in electrolytes has been explained by secondary influences of
electrolysis', and, therefore, does not stand in any relation to
what I have called unilateral conductivity. The unipolar conduc-
tivity of flames has not yet been satisfactorily explained. If my
supposition is correct, and if we must look to the air condensed
on the surface of the wires for the explanation of unilateral con-
ductivity, it will most likely prove to be closely allied to the
unipolar conductivity of flames.
VIIL Conclusion,
The result of the foregoing investigation may be perhaps best,
stated as follows *^— *
Phil. Moff. S. 4. Vol. 48. No. 818. Oct. 1874. S
Digitized by VjOOQIC
258 Lord Baykigh tm the VHrMHam of
The current produced by an eledramotive force m a circuit
compoeed entirely of copper wiree joined together by maosf of
Unding^ecrewi may, under certain eircumttancet, be different frmn
the current produced by the eame electromotive force acting in the
opposite direction.
I have called this phenomenon " unilateral condnetirity;^ and
I have tried to bring it into connexion with known facts. Hie
most plausible explanation seemed to me to be^ that a thin layer
of air may sometimes intervene between the two wires which
are screwed together. This explanation has been confirmed by
some experiments. Other experiments have shown that the ex*
planation is insufficient. I do not think that the evidence is
sufficiently strong to abandon altogether an explanation which
seems to agree so well with the most characteristic features of
the phenomenon. Secondary causes may intervene which pre*
vent the phenomenon from being formed. I suggest the dif-
fusion of the gases into the wires as such a secondary pheno-
menon. E£Fects which are so unstable, however, are never
explained by a simple set of experiments. They will only be
satisfactorily explained by a number of observations from dif-
ferent experimenters. It is, I hope, a sufficient justification for
the publication of the above experiments if they draw the atten*
tion of physicists to a class of pnenomena which sometimes may
seriously interfere with their measurements.
XXXYU. On the Vibrations of Approximately Simple Systems.
By LoKD Batleigh, M.A., F.H.S.'^
IN a paper with the above title, published in the Philosophieal
Magazine for November 1873, 1 drew attention to the fact
that when the natural vibrations of a system are thoroughly
known, the effect of a small variation in the system in changing
the types and periods of vibration may be readily calculated by
a general method. In particular I proved that the altered pe-
riods may be found from the new values of the potential and
kinetic energies on the hypothesis that the types are unchanged,
subject to an error of the second order only. The present note
shows how a farther approximation may be made, and how a
similar method may be applied to a system subject to small dis-
sipative forces.
If ^p ^^ &c. be the normal coordinates of the original system,
the expressions for the kinetic and potential energies are
T=i[l]*?+4[2]^i+
* Communicated by the Author.
• • • >T
f .... (1)
Digitized by VjOOQ IC
(2)
Jfproximaiefy Single Syiiems. 259
Now let the system be dightly varied, so that T and Y become
T+CT=i([ll +S[1])^!+ . . . +8[12]^i^,+ • • • .
V+8V=i({l} + 8{l}>I+...+8{12}^i^,+ ...,
giving for the equations of vibration of the altered system
+ ...=0,
(S[12]D«+8{12}>i + ([2]D«H.8[a]D«+{2} + 8{2}>«
+ ...=0,
&c.
In the original system one of the natural vibrations is that
denoted by the sole variation of if>^. In the altered system this
will be accompanied by simultaneous small variations of the
other coordinates. If the whole motion vary as cos Pft, we get
from the sth equation, as was proved in the paper referred to,
an equation which may be regarded as determining approximately
the character of the altered types of vibration.
Now the rth equation of (2) gives
i/>r(-/>J[r]-pj8[r] + {r}+8{f}) + .-. + ^.(-p;8M
+ 8{r*}>+...=0. (4^
Using in (4) the values of <f>t : ^^ given in (3), we get for the
value ofjE>Jj^
' „«- M + 8{r} (;>;gW-8{r.}X . . (g)
''' [r].+ S[r] [r]M{/»;-i>;)
in which the summation extends to all values of $ other than r.
The first term in (5) gives the value of fl calculated withoujt
allowance for the change of type, and is sufficient when the square
of the alteration in the system may be neglected. If pr f^^r to
the gravest tone.of the system, pi— pi is always positive, and the
term of the second order in (5) is negative, showing that the
calculation founded on the unaltered type gives in this case a
result which is necessarily too high.
If obly the kiiietic energy undergo variation,
w
S2
Digitized by VjOOQ IC
(8)
260 Lord Rayleigh on the Vibrations of
As an example we may take a uniform string of length / and
density p, carrying a small toad m at its middle point. If y be
the transverse displacement at point x,
the origin of x being at one end. In this case for the gravest
tone we have
8T=im(<^',-(^8+^5-...)S
so that
Accordingly
since pjjpj— pj=l :«*— 1.
Fr here denotes the value of/),, when there is no load.
Now
«*— 1 *— 1 *+l
in which the values of s are 3, 5^ 7> 9> &c. Accordingly
■^zTi^'i* • • .^ • • • • (y)
and therefore
pJ=P»{l-^ + ^' + cube«}, . . (10)
which gives the pitch accurately as far as the square of the ratio
m:lp,
l^e free vibrations of a svstem subject to dissipation-forces are
determined in general by the equations
^#-1-^-' • • • • <")
where\ T and V are as before^ and F, called the dissipation-func-
t^n, is of the form
* See ft paper " On lonie General Tlieorcms relating to Vibrations,"
Mathematical Society's Proceedings^ June 1873.
Digitized by VjOOQ IC
Approximately Simpk Systems^ 261
3y a suitable transfcHrmation any two of the functions T, P, V
can be reduced to a sum of squares^ but not in general all three.
When all three occur^ the types of vibration are more complicated
than those of a conservative system, or of that of a dissipative
system with one degree of freedom. When, however, the fric-
tional forces are small, as in many important applications they
are, it is advantageous to proceed as if the system were conser-
vative, and reduce T and V to sums of squares, leaving F to take
its chance. In this way we obtain equations of the form
in which the coefficients (11), (22), (12), &c. arc to be treated
as small.
Let the type of vibration considered be that which differs little
from the sole variation of ^,., and let all the coordinates vary as
c'r', where pr will be complex, as also the ratios of the coor*
dinates. From the ^ equation^
(fM + {*}>.+ (^*)pA+ • • . =0,
we get, by neglecting the terms of the second order,
^''^^ w^^wv ' • • * ^ ^
which determines the alteration of type. Although p is com-
plex, the real part is small compared with the imaginary part ;
and therefore (14) indicates that the coordinates ^, have appi*oxi«>
mately the same phase, and that phase a quarter period different
from that of ^y. The rth equation gives, by use of (14),
i';W+{r}+(rK-2-^|^=0, . . (15)
from which it appears that^^r may be calculated approximately
from the equation
ir-\p\-\-{r)Pr+\r)=0; .... (16)
that is, as if there were no change in the type of vibration. The
rate at which the motion subsides will not be altered, even though
the terms of the second order in (15) be retained.
The reader mav apply these formulse to the case of a uniform
string whose middle point is subject to a small retarding force
proportional to the velocity.
It is scarcely necessary to point out that these methods apply
to other physical problems than those relating to the vibrations
Digitized by VjOOQ IC
262 Mr. W. B. Davis an m Mtthdd oflUiairaiing
of materitl syttemt* For the free motioii of heat in a eondoetor^
we obtain equations eorresponding to those of materisl systona
which are supposed to be devoid of inertia« The funetioiiB F and
y may thus be reduced to sums of squares ; and the effect of a
small variation in the system may be investigated by methods
parsllel to those employdl in the present paper.
TerKng Pbce» Withsm,
September 11, 1874.
XXXVIIL On a simple Method of Illustrating the chief Pheno-
tnena of Wave-Motion by means of Flexible Otris. By the late
W. S. Davis, FJt.A.S.^ Derby*.
[VTith a Plste.J
THE simple methods about to be described, of exhibiting the
chief phenomena of wave-motion, were suggested during
some experiments lately made by the author on the refraction of
liquid waves t* These experiments consisted in the production
of waves on the surfaces of two liquids of different densities,
lying side by side : on agitating the surface of either liquid,
waves were produced whicn passed from one liquid to the other,
at the same time undergoing changes in amplitude, lengthy and
form of front. In preparing diagrams to represent these phe-
nomena it became necessary to make drawings of vertical sec*
tions through the two liquids, perpendicular to their line of
separation.
The appearance presented by the sinuous lines on these dia«
grams immediately suggested that a similar appearance could be
exhibited by means of waves on flexible ooras. India-rubber
tubes, variously suspended, and both empty and loaded, were
tried without satisfactory success ; the waves moved too quickly
to be well observed, and the reflected waves interfered with the
direct cfne^. Further experiments led the author to devise the
simple apparatus now exhibited, which, however, has been made
to serve for many other illustrations of wave-motion in addition
to those it was at first intended to show.
The apparatus consists essentially of: — (1) a piece of stout
board about 20 feet long and 9 inches wide, which should be
Cted black; and (2) three or four ropes, which must be both
y and flexible : the ropes used by builders for securing their
sctffibldiDg have been found to answer very well^ especially if
they have been in use some time. To enable the eye to readily
♦ Read before the Physical Society, May 9, 1874. Commumcated by
the Society,
t Bee Brit. Assoc. Report, 1873.
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Digitized by VjOOQ IC
Phenomena of JFwe^MoHon by memo of Flexible Ccrde^ d63
distinguish any ptrtieolar rope when two or more are used
together^ it is well to coyer the ropes with di£ferently coloured
fabrics^ say red^ bluci and green. A few other accessories are
necessary^ which will be described as they are required*
By means of this apparatus wares may be produced which
more slowly enough to be readily examined by the eye. The
chief phenomena of wave-motion which can oe shown are as
follows :—
1. TroMsmiseion of a Wave. — One end of a rope^ a few feet
longer than the boards is fixed to a hook at the end of the board.
The free end of the rope is then taken in the hand^ and^ the
the rope being quite slacks a sudden up-and-down movement of
the hand is made. A protuberance is thus formed which moves
very slowly along the rope, presenting the appearance shown in
Plate y. fig. 1*
A single up-and-down movement produces a wave consisting
of a crest only, the trough being suppressed by the board ; if,
however, with the rope very slack, the hand be moved up and
down very quickly and energetically, a series of waves, consisting
of both crest and trough, are produced (fig. 2).
2. Amplitude and Wave-length. — Waves having any length,
from 1 to 6 or 7 feet, and amplitudes of similar dimensions, are
easily produced by properly controlling the rapidity and energy
t)f the motion of the hand.
8. Decrease of Intensity with Dietance. — ^This is illustrated by
a succession of waves produced by the well-timed motion of the
hand (fig. 2). The actual decrease of amplitude in this case is,
of course, due to the loss of energy by friction, and not to lateral
-spreading.
4. Relation of Velocity to Elasticity, — Two similar ropes, one
covered with red and the other with blue, are laid side by side
along the board and fastened to hooks at one end. The free
ends of the ropes are held in the hand, with the finger between
them, and, care being taken that they are equally loose, the hand
is moved up and down as usual. The result is that a wave of
the same height and length is produced on each rope, and the
two waves travel side by side to the ends of the ropes. The ex-
periment is repeated with one rope somewhat tighter than the
other, when the wave on the tighter rope is observed to travel
faster than that on the looser one (fig. 3). On continuing to
tighten the rope the velocity of the wave is more and more in-
creased, and may be caused to reach the end of the rope a whole
length or more before its fellow.
5. Relation of Velocity to Density, — ^To exhibit this relation a
* The length of the board in the figures \b drawn to a much smaller
'scale than the other parts.
Digitized by VjOOQ IC
264 , Mr. W. S. Davis an a Method of lUuUrating
loaded rope is required. That now used has strung upon it m
number of rings of lead cut from a leaden water-pipe; these
are placed about 6 inches apart, and are covered with india-
rubber bands to prevent their making unpleasant noise. IW
loaded and an unloaded rope are laid on the board side by side,
and fixed at one end. Then^ taking care the tension is equal
in the two ropes, waves are simultaneously generated on theroi
as before described. It is then observed that the wave on the
loaded rope lags considerably behind the other (fig. 4). By suffi-
ciently tightening the loaded rope the velocity of its waves may
be made equal to, or even greater than that of the waves of tl^
unloaded rope. This may be used to explain whv the velocity
of sound in water is greater than in the much less oense medium^
air.
6. Transmission of Waves from one Medium to another of dif-
ferent Density. — The loaded cord is attached end to end to one
much lighter than itself; the united cords are laid on the board
with the splice at about the middle of its length. Then, fasten-
ing the end of the lighter cord, waves are generated on the
heavier one. These waves pass onwards to the lighter cord, on
reaching which they acquu*e greater amplitude, velocity,, and
length (fig. 6). If the heavier cord be fixe4 and waves be gene-
rated on the lighter one, the reverse changes to those just stated
occur on the waves reaching the heavier cord. It is an interest-
ing experiment to transmit waves along a succession of three or
more cords alternately heavy and light. With three cords joined
end to end, the middle one being heavier than the others, a good
illustration is produced of the changes of velocity, length, and
amplitude which setherial waves unaergo in passing perpendi-
cularly through a medium with parallel faces.
7. Separation of a Wave into two or more smaller Waves. — A
single cord extending half the length of the board is joined to a
double one extending the other half. Waves are transmitted
from the single cord to the double one ; on reaching the latter
each wave divides in two, one wave traversing one part of the
double cord, and the other wave the other part. By giving each
part of the double cord a different tension, the velocity of the
waves will be different in each (fig. 6). The waves on the double
cord may be made to move in planes at right angles to each
other by the use of proper guides, thus furnishing an illustration
of some of the phenomena of double refraction.
8. Superposition and Interference. ^The same arrangement is
used as in 7, but the waves are transmitted from the double
cord to the single one. With equal tension in each part of the
double cord, the waves simultaneotusly produced on each part run
side by side until they enter the single cord^ when they are su-
Digitized by VjOOQ IC
Phenomena of Wave-motion by iheans ofFUiXiible Cords. 265
perposed and produce a wave of doable amplitude. One half of
the double cord may be tightened until its wave reaches the single
cord half a wavers length before the wave on the other half ^
when interference occurs^ there being little or no lateral motion
to be observed in the single cord.
- 9. Plane of Waves, — In the experiments previously described
the waves were transmitted in a vertical plane ; but by properly
directing the motion of the hand, the waves may be transmitted
in planes variously inclined to the board, or in a plane parallel
with it. Waves in space of three dimensions, corresponding to
circularly polarized light, are produced by rapidly and regularly
moving the hand in a circle, the cord then taldng the form
shown at the right of figs. 7 and 9.
10. Polarization. — A series of flat boards are used as guides;
which are clamped on the long board. These are shown in
figs. 7, 8, 9. The vertical and oblique guides are each in two
pieces, which are so approximated to each other as to just allow
the cord to move freely between them. The horizontal guide is
in one piece only. The vertical and horizontal guides being
fixed as shown in figs. 7 and 8, waves in a vertical plane are
transmitted from that end of the rope nearest the vertical guides ;
the waves then pass freelv through the vertical guides^ but are
completely stopped by the horizontal one. Waves in a hori«
zontal plane transmitted from the other end of the apparatus
pass the horizontal guide, but are stopped by the vertical ones
(fig. 8). Waves in an oblique plane transmitted from either end
are resolved by the nearest guide into a component in its own
plane and a component at right angles which is suppressed;
the former passes on and is stopped by the next guide. Circularly
polarized waves on reaching the guides are similarly resolved
(fig. 7). ,
11. Depolarization, — A pair of oblique guides are required in
addition to those described in 10. The arrangement of these is
shown in fig. 9, which needs no further explanation. The waves
are supposed to proceed from right to left. With a single cord
as in fig. 9, or with a partly double one as in fig. 6, an endless
variation of experiments relating to polarization maybe produced.
12. Radiation and Absorption. — ^A rod of iron about 2 feet
in length, having an eye at the centre and at each end, is fixed
by means of a screw or pin through the central eye to an up*
nght support of wood clamped at about the middle of the board
(fig. 10). The iron rod must be able to rotate freely about the
pin in a vertical plane parallel to the board, but in no other
plane. Attaching a cord to one end of the iron rod and conti-^
nuing it to the end of the board, a series of properly timed waves
are sent fdOPg itj when the rod vibrates in synchronisni with th^
Digitized by VjOOQ IC
waves. If a second cord be attached to the other end of the
rod and waves be transmitted as before^ the vibrations of the
rod set up waves in this cord which correqKmd in period and
length to those on the first cord^ thus furnishing an illustration
of the reciprocity of radiation and absorption.
The autnor has reason to think that, as nearly all the above-
described illustrations have been devised during the last twdve
months, the method is capable of much further development and
greater perfection.
XXXIX. Researches in Acoustics. — ^No. V.*
By Alfred M. MATKRf*
1. An Experimental Confirmation of Fourier's Theorem as ap^
plied to the Decomposition of the Vibrations of a Comporiie
Sonorous Wave into its elementary Pendulum^vtlfrations^
A SIMPLE sound is a sound which has only one pitch. Such
a sound is produced when^ with a bow, we gently vibrate the
prongs of a tuning-fork and bring them near a cavity which ir-
sounds to the fork's fundamental tone. An almost pure simple
sound can be obtained by softly blowing a closed organ-pipe.
On examining the nature of the vibratory motions of the
prongs of the fork:^ and of the molecules of air in the resound-
* This paper it the fifth in the series of those on Aeoustict aliesdy
published m the Philosophical Magaxine. The preceding papers, however*
were not numbered.
t Communicated by the Author, with corrections, from Silliman*s Ame-
rican Journal for August 1874.
Sections 1, 2, 3, b, 6, and 7 of this paper were read before the National
Academy of Sciences during the Session of Norember 1873. Section 4 was
read before the Academy on April 21, 1874.
X In my course of lectures on Acoustics, I thus show to my students
that the prong of a tuning-fork vibrates like a pendulum : — I take two of
Lissajous's reflecting forks, giving, say, the major third interval, and with
them I obtain on a screen the curve of this interval in electric light. On
a glass plate I have photographed the above curve of the major Uiird pas-
sing through a set of rectangular coordinates formed of the sines of two cir-
cles whose circumferences are respectively divided into 20 and 25 equal
parts. I now place this plate over the condensing-lens of a vertical lantern
and obtain on the screen the curve, the circles, and their net of coordinates.
Suspended over the lantern is a Blackburn's compound pendulum* which is
so constructed that its^' bob " cannot rotate around its axis. The bob is
hollow, and a curved pipe leads from its bottom to one side of the pendulum.
The pendulum is now defiected into a plane at 45*^ with its two rectangu-
lar planes of vibration, so that the end of the curved pipe coincides with the
beginninff of the curve over the lantern. The bob of the pendulum is fas-
tened witn a fine cord in this position, and fine hour-glass sand is poured
into it j the cord is now burned, and the sand is delivered from the pipe
as the swinging pendulum gives the resultant of its motions in the two
planes of vibratioB, while the photograph^ ^rve o^tbe. lantern is pro-
Digitized by VjOOQ IC
Fh>f. A. M* Mayer's Eeitatehei m Acauftia. 267
ing eavity* and in the cloeed organ-pipe f, we find that each of
these vibrations follows the same law of reciprocating motion
as governs the vibrations of a freely swinging pendulum. But
other bodies, for instance the free reeds of organ-pipes and of
melodeonsj^ vibrate like the pendulum ; yet we can decompose
the vibrations they produce in the air into many separate pen*
dulum-vibrations^ each of which produces in the air a simple
sound of a definite pitch* Thus we see that a pendulum-vi-
brating body^ when placed in certain relations to the air on
which it acts, may give rise to highly composite sounds. It is
therefore evident that we cannot always decide as to the simple
or composite character of a vibration reaching the ear solely
from the determination of the motion of the body originating
the sound, but we are obliged to investigate the character of the
molecular motions of the air near the ear, or of the motion of a
point on the drum of the ear itself, in order to draw conclusions
as to the simple or composite character of the sensation which
may be produced by any given vibratory motion. Although we
cannot often detect in the ascertained form of an aerial vibration
all the elementary pendulum-vibrations, and thus predetermine
the composite sensation connected with it, yet if we find that
the aerial vibration is that of a simple pendulum, we may
surely decide that we shall receive from it only the sensation
of a simple sound. Thus, if we arm the prong of a tuning-
fork with a point, and draw this point on a btmp-blackened
surface with a uniform motion and in a direction parallel to
the axis of the fork, we shall obtain on the surface a sinusoidal
or harmonic curve §; and this curve can only be produced
by the prongs of the fork vibrating with the same kind of
gressively covered with the gand if the times of the two vibrations of the
pendulam are to each other as 4 to 5.
* Helmholtz, Tbnen^findmngen, 1857> p. 75. Grelle's J<mm,fUr Math.,
ToL Ivii.
t See Mach's Optisch-ahutische Versuche, Prag, 1873, p. 91. Dig
Stroboskopische Darstellung der Luftschvoingvngen.
X The Rey. S. B. Dod, one of the trustees of the Stevens Institute, has
recently made an experiment which neatly shows this : — He silvered the
tips of two melodeon-reeds, and then vibrated them in planes at right angles
to each other, while a beam of light was reflected from them. The rdbul-
tant figure of their vibrations is the same as that obtained by two Lissajous's
forks placed in the same circumstances and having the same musical inter-
val between them as that existing between the reeds.
§ The equation of this curve is y = a sin (^r^+ « ) • The length, on the
axis, of one recurring period of the curve is X ; the constant a is the maxi-
mum ordinate or amplitude. The form of the curve is not affected by a ;
but any change in its value slides the whole curve along the axis of x. It
is interesting to observe that this curve expresses the annual variation of
temperature in the temperate zones.
Digitized by VjOOQ IC
268 Prof. A. M. Meyer^s Researches in Aeouatiesr
motion as that of a freely swinging pendnlum. If we now brin^
this vibrating fork near the mouth of a glass vessel whose mass
of air responds to the tone of the fork, and, by the method of
Mach, examine the vibratory motions of the air, we shall see it
swinging backward and forward; and by combining these vibra*
tions with the rectangular vibrations of forks placed outside of
the vessel we shall obtain the curves of Lissajous* If the mem-
brane of the drum of the ear be placed in connexion with the
resounding cavity, it must necessarily partake of the motion of
the air which touches it, and ultimately the auditory nerve fibrilbe
are shaken in the same manner, and we receive the sensation*
of a simple sound. Here the mind naturally inquires the reason
of this connexion existing between the sensation of a simple
sound and the pendulum-vibration. It has always appeared to
me that the explanation of this invariable connexion is that the
pendulum-vibration is the simplest vibratory motion that the
molecules of elastic matter can partake of, and that the con-
nexion of the sensation with the mode of vibration is the con-
nexion between the simplest sensation perceived through the
intervention of the trembUug nerves, and the simplest vibration
which they can experience. Indeed the pendulum-vibration is
the only one which produces the sensation of sound ; for if any
other recurring vibration enters the ear, it is decomposed by the
ear into its elementary pendulum- vibrations ; and if it cannot
be so decomposed, then the given vibration is not recurring and
does not produce in us the sensation of sound, but causes that
which we denominate noise. This remarkable connexion be-
tween a simple sound and the pendulum or harmonic vibra-
tion, together with the fact of the power of the ear to decompose
the motions of a composite sonorous wave into its vibratory
elements, was thus distinctly enunciated by Ohm : — The ear has
the sensation of a simple sound only when it receives a pendulum-
vibration ; and it decomposes any other periodic motion of the air
into a series of penduhtm-vibrations, each of which corresponds to
the sensation of a simple sound.
We have seen that the harmonic curve is the curve which
corresponds to the motion which causes the sensation of a sim-
ple sound ; but a molecule of vibrating air or a point on the
tympanic membrane may be actuated by vibratory motions
which, when projected on a surface moving near them, will
develop curves which depart greatly from the simplicity of the
harmonic, or curve of sines f; but nevertheless these curves
* See Helmholtz on the distinction between a sensation and a perception*
Tonempfindungeny p. 101.
t In section 6 of this paper I have constructed several important curves
corresponding to composite vibrations.
Digitized by VjOOQ IC
Prof. A. M. Mayer's Researches in Acoustics, 269
will always be periodic if the sensation corresponding to their
generating motions is that of sound. Now Fourier has shown^
and states in his theorenii that any periodic curve can always be
reproduced by compounding harmonic curves (often infinite in
number) having the same axis as the given curve and having the
lengths of their recurring periods as 1^ ^, i, {, ke, of the given
curve ; and the only limitation to its irregularity is that its ordi-
nates must be finite^ and that the projection on the axis of a
point moving in the curve must always progress in the same di-
rection. Fourier demonstrates that the given curve can only
be reproduced by one special combination, and shows that, by
means of definite integrals, one can assign the definite sinusoids
with their amplitudes and differences of phase. Now Helm-
hoitz* has shown that di£ferences of phase in the constituent
elementary sounds do not alter the character of the compo-
site sound, and, therefore, that although the forms of the curve
corresponding to one and the same composite sound may be
infinite in variety (by reason of differences in phase in the com-
ponent curves), yet the composite sound is always resolved
into the same elements. This experimental result of Helmholtz
also conforms to the theorem of Fourier in reference to the
curves projected hj such motions ; for he has shown that only
one series of sinusoidal resolution is possible.
Fourier's theorem can be expressed as follows : — The con-
stants C, G|, Cqy &c., and ay, a^, &c., can be determined so that
a period of the curve can be defined by the following equation f : —
y = C + C,sin(?^+«,) + C,sin(2?^+^,)
+ ...
But Fourier's theorem is the statement of a mathematical
possibility; and it does not necessarily follow that it can be im-
mediately translated into the language of dynamics without
experimental confirmation ; for, as Helmholtz remarks, '^ That
mode of decomposition of vibratory forms, such as the theorem
of Fourier describes and renders possible, is it only a mathe-
matical fiction, admirable because it renders computation facile,
but not corresponding necessarily to any thing in reality ? Why
consider the pendulum-vibration as the irreducible element of
all vibratory motion ? We can imagine a whole divided in a
multitude of different ways; in a calculation we may find it con-
venient to replace the number 12 by 8 + 4, in order to bring 8
* Tonenmfindungenj p. 190 f/ seq.
t For other and more convenient forms of expression of this theorem,
as well as for a demonstration of it, see pp. 62 and 60 of Donkin's 'Acous-
tics'— the most admirable work ever written on the mathematical theory of
sound*
Digitized by VjOOQ IC
270 Prof. A. M. Mayer's Ruemrches m Acauitics.
into view ; but it doet not neoesMtrily follow that 12 should al-
ways and necessarily be considered as the sum of 8+^ Ia
other cases it may be more advantageous to consider the number
as the sum of 7+5.
'' The mathematical possibility^ esUblished by Fourier, of de*
composing any sonorous motion into simple vibrations, cannot
authorise us to conclude that this is the only admissible mode
of decomposition, if we cannot prore that it has a signification
essentially real. The fact that the ear effects that decomposition,
induces one, nevertheless, to believe that this analysis has a
signification, independent of all hypothesis, in the exterior
world. This opinion is also confirmed precisely by the Aict
stated above, that this mode of decomposition is more advanta-
geous than any other in mathematical researches ; for the me-
thods of demonstration which comport with the intimate nature
of things are naturally those which lead to theoretic results the
most convenient and the most clear.'^
The theorem of Fourier, translated into the language of dy-
namies, would read as follows : — *' Every periodic tfihraiory motion
can ahiHtt/s, and always in one mannery be regarded a$ the turn of
a certain fmnber ofpendulum-vibratione/^
Now we have seen that any periodic vibratory motion, which
has the proper velocity, will cause the sensation of a musical note,
and that a pendulum-vibration gives the 'sensation of a iimple
souud'*^; therefore, if Fourier's theorem is applicable to the
composition and decomposition of a composite sonorous wave, ii
will be thus related to the phenomena of sound: — ^^ Every w-
bratory motion in the atutitory canal, corresponding to a musical
sound, can always, and always in one manner, be considered as
the sum of a certain number of pendulum-vibrations, corresponSng
to the elementary sounds of the piven musical note.**
Heretofore we have called in the aid of the sensations (as*
sumed to be received through the motions of the covibrating
parts of the ear) to help us in our determination of the simpk
or composite character of a given vibratory motion ; but Fou«
rier^s theorem does not refer to the subjective effects on the
organ of hearing, the dynamic function of whose parts are yet
♦ Professor DonkiD; in his 'Acoustics/ Oxford) 1870, p. 11, advises tk«
use of tone to designate a simple sound, and the word note to distinguish
a composite sound. His reasons are *^ that tone (Gr. r6poi) really means
tension, and the efiect of tension is to determine the pitch of the sonad of s
string;" while a musical note is generally a composite sound. Professor
Donkin further states, " Helmholtz uses the words Kkmg and Ton to signify
compound and simple musical sounds. We have followed him in adoptmg
the latter term ; but such a sound as that of the human voice could haidfy
in Enslish be called a olanjf, without doing too mudi vi<;4ence to established
Digitized by VjOOQ IC
Prof. A. M. Mayer's Re$earehe$ in Acausties. 271
very imperfectly understood. Ohm's theorem, on the other
hand, refers entirely to these sabjective phenomena of the ear's
analysis of a complex sensation into its simple elements. As
Fourier's theorem refers only to the decomposition of a com-
posite recurring vibration intQ its elementary pendulum-vibra-
tions, it has nothing to do with the physiological fact of the co-
relation of the pendulum-vibrations and the simplest auditory
sensation; though this well-ascertained relation gives us the
privilege of using this sensation as an indicator of the existence
of an aerial pendulum-vibration. Hence, as Fourier's theorem
IB entirely independent of our sensations, we must endeavour to
verify it directly by experiments, which must perform the actual
decomposition of the composite periodic motion of a point into
its elementary pendulum-vibrations. But many difficulties pre*
sent themselves when we would bring to the test of experiment
the dynamic signification of Fourier's theorem. For example,
the composite sound-vibration, on which we would experiment,
emanates from a multitude of vibrating points; parts of the
resultant wave-surface differ in their amplitudes of vibration;
while points equally removed from one and the same point of
the body originating the vibrations, may differ in their phases of
vibration; so that when such a wave falls upon oovibrating
bodies which present any surface, the effects produced are the
result of extremely complex motions. The mind sees at once
the difference between this complicated coneeption and the sim*
pie one embodied in the statements of the dynamic application
of Fourier's theorem.
As the mathematician decomposes seriatim every point of the
recurring curve into its harmonic elements, so the physicist, in
eonfirming the dynamic application of Fourier's theorem, should
decompose into its simple pendulum-vibrations the composite
vibratory motion which such a curve represents, and indeed re*
froduces when it is drawn with a uniform motion under a slit in
a diaphragm which exposes to view only a point of the curve at
once. Therefore only one vibrating point of the composite so-
norous wave should be experimented on; and the composite vi<^
bratory motion of this point should be conveyed along lines to
Joints of elastic bodies which can only partake of simple pen*
ulum-vibrations. All of these essential conditions I have
succeeded in securing in the following arrangement of ap-
paratus.
A loose inelastic membrane (thin morocco leather does well)
was moimted in a frame and placed near a reed-pipe ; or, as
in other experiments, the membrane was placed over an opening
in the front of the wooden chamber of a (ireni^'s free-reed pipe.
The ends of sev^ fine fibre* from a silk-worm^s ooooou were
Digitized by VjOOQ IC
272 Prof. A. M. Mayer's Researches in Aeaustics.
brought neatly together and cemented to one and the same point
of the membrane, while the other ends of these fibres were at-
tached to tuning-forks mounted on their resonant boxes, as
shown in fig. 1. In the experiment which I will now describe
Fi«- 1.
eight forks were thus connected with one point of the membrane.
The fundamental tone of the pipe was Ut,, of 128 vibrations per
second ; and the pipe was brought into accurate unison with a
fork giving this sound 'l^. The forks connected with the mem-
brane were the harmonic series of Ut,, Vt^, Sol,, Ut4, Mi4, Sol4y
Bi", Utg. In the first stage of the experiment we will suppose
that the fibres are but slightly stretched ; then, on sounding the
pipe, all the fibres at once break up into exquisite combinations
of ventral segments. If the sunshine fall upon a vibrating fibre
and we look on it obliquely in the direction of its length, we
shall see ventral segments superimposed on ventral segments in
beautiful and changing combinations. On gradually tightening
the fibres, we diminish the number of their nodes ; and on reach-
ing a certain dgeree of tension with fibres 1 m. long, I have seen
them all vibrating with single ventral segments. On increasing
the tension, the amplitudes of these single segments gradually
diminish and at last disappear entirely, so far as the unaided
eye caii discern ; and then we have reached the conditions re-
quired in our experimental confirmation.
The point of the membrane to which the fibres are attached
is actuated by a motion which is the resultant of all of the
elementary pendulum-vibrations existing in the composite
sonorous wave ; and the composite vibrations of this point are
* Since the number of beats per second ffiyen by any harmonic (of a
pipe out of tune with its harmonic series of forks) will be as the order of
the harmonic, it is better to tune a reed to unison with a fork giving one of
its higher harmonics* I generally used the Sol, fork, or the 3rd harmonic.
Digitized by VjOOQ IC
Prof. A. M. Maycr*8 Researches in Acoustics. 273
sent through each of the fibres to its respective fork. Thus
each fibre transmits to its fork the same composite vibratory
motion^ while each fork can onl^ vibrate so as to give the
simple pendulum-vibration of a simple sound ; for each fibre is
attached to its fork at a point which lies in the upper node of
the s^ments into which the fork divides when it gives its
higher harmonic. Now, if Fourier's theorem has '^ an existence
essentially real/^ any fork will select from the composite vibra-
tory moticm which is transmitted to it that motion which it
has when it freely vibrates; but if its proper vibration does not
exist as a component of the resultant motion of the membrane^
it will not be m the least affected. Now this is exactly what
happens in our experiment ; for when the pipe is in tune with
the harmonic series of forks, the latter sing out when the mem-
brane is vibrated ; but if the forks be even slightly thrown out
of tune with the membrane, either by loading them or by alter-
ing the length of the reed, they remain silent when the sounding-
pipe agitates the membrane and the connecting fibres'*^* Thus
have I shown that the dynamic application of Fourier's theorem
has " an existence essentially real.''
It is indeed very interesting and instructive thus to observe
in one experiment the analysis and synthesis of a composite
sound. On sounding the reed it sets in vibration all the forks
of the harmonic series of its fundamental note ; and after the
reed has ceased to sound, the forks continue to vibrate, and
their elementary simple sounds blend into a note which approxi-
mately reproduces the tiuibre of the reed-pipe. If we could by
any means obtain all of the elementary vibrations and have them
with their relative intensities correctly preserved, we should have
an echo of the sound of the reed after the latter had ceased to
vibrate ; but the impossibility of thus obtaining the highest com-
ponents of the reed, and the difficulty of reproducing the relative
intensities of the harmonics in the covibrating forks, allow us
but partially to accomplish this effect.
2. An Experimental Illustration of Helmholtz's Hypothesis of
AuMtion.
The experiment which we have just described beautifully illus-
trates the hypothesis of audition framed by Helmholtz to account
for this, among other facts — ^that the ear can decompose a
composite sound into its sonorous elements. Helmholtz founds
his hypothesis on the supposition that the rods of Corti, in the
ductus cochleaiis, are bodies which covibrate to simple sounds-*
* See section 5 of this paper for an account of the degree of precision
of this method of sonorous analysis.
Pm, Mag. S. 4. Vol. 48. No. 318. Oct. 1874. T
Digitized by VjOOQ IC
974 Prof. J. J. M&ller on m Uedumatl PrineipU
■omewhit, I imigine, ai lodkd strings^ of graded kngtlis and
diameters would aet in itmilar drenmstanoes. The Tibrntiona
of the eompoeite wave fall upon the membrane plaeed near the
reed at they fall upon the membrane of the tympanum ; and
these vibrations are sent through the stretched fibres (or ddicate
splints of rye-straw, which I have sometimes used) from the
membrane to the tuned forks, as they are sent firom the mem-
brana tympani through the ossicles and fluids of the ear to the
rods of Corti. The composite vibration is decomposed into its
vibratory elements by the covibration of those forks whose vi*
bratory periods exist as elements of the composite wave*moti<m j
so the composite sound is decomposed into its sonorous elements
by the oovibrations of the rods of Corti, which are tuned to the
elementary sounds which exist in the composite sonorous vibra*
tion« The analogy can be carried yet further by placing Uie
forks in line and in order of ascending pitch, and attaching to
each fork a sharply*pointed steel filament. If the arm be now
stretched near the forks, so that the points of the filaments nearly
toueh it at pmnts along its length, then any fork will indicate
its covibration by the fact of its pricking the skin of the anoi
and the localiiation of this pricking will tell us which of the
series of forks entered into vibration. The rods of Corti shake
the nerve-filaments attached to them, and thus specialise the po*
sition in the musical scale <^ the elements of a composite sono-
rous vibration. Thus a complete analog is brought into view
between our experiment and Helmholtrs comprehensive hypo*
thesis of the mode of audition.
[To be continued.]
XL. On a Mechanical Principle retuUing from Hamilton's Theory
qf Motion. By J. J. MCllxb, Profeuor at the Polytechnic
in ZUrichf.
WHEN a system of material points moves under the influ*
ence of forces proceeding from the reciprocal attraction
and repulsion of the points, all the integral equations of the mo*
tion can, as Hamilton has shown|, bcrepresented by the par-
tial differential quotients of a function of the coordinates (the
primary function), in a manner similar to that in which, accord-
ing to Lagrange, its differential equations can be represented by
aid of the partial differential quotients of the force-function.
Therein the primary function satisfies two partial differential
equations ; but even one of these equations, as Jacobi demon-
♦ For ditcnnions of the vibretory phenomena of loaded strings, sec Don-
kin't ' Acoustics,' p. 139, and Ilelmholtz's Tonempfindungen, p, 267.
t Tnnslated from PoggendorflTs Annalen, vol. clii. pp. 10^-131.
J Phil. Trans. 1834, 1835.
Digitized by VjOOQ IC
reiuUingjrom Hamilton^B Theory of Motion. 275
fttrated^ is sufficient for its definition. The primary function is
a complete solution of this differential equation ; and any com-
plete solution of the latter^ analogously differentiated according
to the constants^ gives the system of the integral equations.
Hence, in the Hamilton-Jacobi method, the entire problem is
concentrated into the one integration of the partial differential
equation, in contrast to Lagrange's way of proceeding, in which
only single integrals are found by aid of the known principles*
The integration of the partial differential equation was developed
by Jacobi't^ generally both in the way already pursued by La^
grange and Pfaff, and also by a new and grand method, both of
which methods have been adopted in a series of more recent
works.
The theory above mentioned has recently undergone expan-
sbn in two respects. If the investigation by Hamilton and
Jacobi referred to actual space, for which the element of a line
proceeding from a point is capable of being represented by the
iquare root of the sum of the squares of differentials of the ordi*
nates of the point, Lipschitsf formed a more general conception
of the problem, inasmuch as he assumed the line-element to be
equal to the pi\k root of any real positive form, of the /7th degreCi
of the differentials of any coordinates of the point in question.
The element of its integral corresponding to the primary func«
tion becomes the sum of any form of the pih, degree of the dif-
ferential quotients, taken according to time, of the variables and
any force-function depending only on the variables— this sum
multiplied by the time-element ; so that the problem of mecha«
nics is changed into a perfectly general one of the calculus of
variations. If, further, Hamilton assumed a force-function
which depended only on the coordinates of the moved point, and
if Jacobi extended the investigation to a force-function explicitly
containing the time, Schering j: conceived the problem in this
direction more generally, introducing forces dependent not only
on the position but also on the state of motion of the masses.
This dependence is so chosen that, tmderstauding by R the re^
suiting force, and by dr the virtual displacement of the mass*
points, SR£&* becomes the difference oetween a total variation
and a total derived according to time ; and this generalization ii
at the same time accomplished from Lipschitz's enlarged point
• of view. In it, therefore, motions can be treated which, for in*
* ''Vorletongen iibeir Dynamik: Nora methodus" &c., Borcbsrdt's
Journal, 60.
t "Untersuchung eines Problems derVariationsrechnung," Borcbardt's
Journal, 74.
X Hamilton- Jacobi'sche Tbeorie fiir Krafte, deren Maass von der Bewe-
gungder Korper abhangt/' Abhiindl.derGdtting.Oes.derJVissenschASlS.
T2 .
Digitized by VjOOQ IC
276 Prof. J. J. Mullet on a Mechanical Principle
atance, satisry Weber*^ law, or motions in Ghiass'a and Riemaun's
space of multiple dimensions.
The slight improvement of the physical side of Hamilton's
method stauds far from the high degree at which these analytical
investigations have arrived. An essential peculiarity of it con-^
sists in this — that it passes from a given motion of the svstem
of points to another in a similar manner to that in which La-
grange's process passes from one configuration of the points to
another. The primary function, a definite integral which is ex-
tended over the original motion, undergoes an alteration by the
Variation of the arbitrarv constants of the motion ; and this va-
riation, or that of a similar integral representing the expenditure
of the force, is given by Hamilton's symbolic equations of mo-
tion. Hence Hamilton's method differs, secondly, from La-
grange's (in which the force-function changes according to the
elements of the given motion) in the same way as the variation
differs from the differentiation of the functions. This second
aspect of it could not but lead immediately to a new treatment
of the perturbations, which has by Hamilton, Jacobi, and Sdie-
ring.been developed into a series of new systems of pertnrbation-
formule. . Only the above-mentioned application of the variation
of the motion, which is in principle only a particular way of re-
presenting the latter, is not the essential of the new view ; that
must much rather be sought in similar principles to those on
which the ordinary differential equations of the mechanical pro-
blem are based. It is true that one signification of these prin-
ciples, the representation of individual integrals, does not here
iM>me into consideration in the indicated general process of inte-
gration ; their physical meaning, however (independent of the
other), which was proved most evidently in the proposition of
4he vis viva, especially with the generality given to it by Helm-
lioltz, remains here also; and this iustifies an examination of it.
Such an examination of the physical aspect of Hamilton's
method is attempted in the sequel. It appeared the more re-
quired, as the endeavours of physicists to deduce the second
proposition of the mechanical theory of heat in a similar manner
as the first, from purely mechanical conceptions, clearly per-
mitted the supposition of a new mechanical principle. Bolts-
mann'i', Clausiusf, and LedieuJ have succeeded in obtaining
from Lagrange's differential equations the proposition mentioned:
it did not, however, like the first proposition, come from a uni-
versal principle ; but, on the contrarVi those investigations led
to new mechanical propositions, which certainly did not possess
♦ Wiener SUiunosberickte, vol. liii.; Po^j. Ann. vol.cxliii. p. 211.
t Pogg. Ann. vol. cxlii. p. 433. Phil, Mi^. S. 4. vol. xlii. p. 161,
J Comptes Rendus, 1873, 1874,
Digitized by VjOOQ IC
resuliingfrom Hamilton's Theory of Motion. 277
the amplitude of the principle of the vis viva. An attempt by
Szilv* to get the proposition out of Hamilton's treatment of thq
subject comes nearer to the above notion ; only, not to mentiop
that, on account of a limitation adhering to the form in which it
has hitherto appeared, it could not lead to the general deduction
required, it does not approach more closely the physical side of
this method.
It resulted from the investigation that the new treatment
satisfies a general principle similar to that satisfied by Lagrange's;
for perfectly coordinate with the proposition of the vis viva is
the following : — In a motion whose equations of condition and
force-function do not explicitly contain the time, let the primarv
function and expenditure of force respectively be denoted by V
and W, so that
-V=r(T-U)rf/, W=r2Trf/,
Jo Jo
understanding by T the vis viva, and by U the force-function ;
and let it be assumed that V may be represented as a function
of the initial and final coordinates and the time, W as a function
of the initial and final coordinates and the energy ; then for
every change of motion occurring during an element of time dt
the relation
dt ^l ht J-""
holds, in which the symbol d signifies the whole of the alteration
which is connected with change of motion, while d denotes all
alterations of V-hW not produced by variations of the coordi-
nates. Therefore^ in every motion whose equations of condition
and force-function do not explicitly depend on /, the change of
the primary function and force-expenditure produced by the
variation of the coordinates alone is =0. The two quantities W
and y are here capable of a physical interpretation similar to that
of T and U. The former has already been designated by Ha-
milton as the vis viva accumulated in the motion ; the significa-
tion of the latter results from a peculiarity of the entire Hamil-
tonian theory of motion : namely, while la micanique analj/"
iique prefers to introduce the forces into the equations of motion,
Hamilton's treatment involves the introduction of the momen-
tary impulses — ^indeed, so that the place of the forces is taken by
those impulses which at each instant are capable of producing
the velocities actually present. Now, in a group of motions,
these impulses can, analogously to the forces, be represented as
negative pai*tial differential quotients of a function of the coor-
* ^ofg' Ann, vol. cxlv. p. 295; vol. cxlix. p. 74. Phil. Mag. S. 4.
vol. xliu. p. 339 ; vol. xlvi. p. 426.
Digitized by VjOOQ IC
278 Prof. J. J. Muller on « Meehankal Prine^U
dinates j and this function is nothing else but the above-defined
primary function of the system. This peculiarity gives to the
primary function a real signification simdar to that obtained by
the force-function in the potential energy, and makes the coor-
dination between the principle of energy and the new proposi**
tion still more evident.
If this proposition was the general principle at which those
investigations of the theory of heat aimed, it must have included
as a special case the second proposition of that doctrine, in the
same way as the principle of energy included the first In this
relation it is remarkable that, applied to the mechanical theory
of heat, it leads direct to the second main proposition as soon as
we make the apparently indispensable supposition that the tem«
perature of bodies is proportional to the vis viva of their mole-
cular motion. Corresponding to this, the principle seems also
capable of a series of further applications like those of the prin-
ciple of energy ; those which will be here given, however, are
limited to the case belonging to the theory of heat.
The proposition cited resulted from the combination of two
long-known mechanical equations. Hamilton, namely, had
given his equations of motion both in reference to the function
y and in reference to the function W ; and the separate results
needed only to be combined, in order at once to furnish the new
one. It would be obtained in the most general form by intro-
ducing the integral elements generalized in the sense of Lip-
schits and Schering. As, however, the essential point was its
application to real physical motions, and it had to be presented
first in its simplest form, I have preferred to give it in connexion
with the older method of Hamilton and Jacobi, which moves en*
tirely on this ground. But then this process must in another
respect be conceived more generally ; for, in every form in whidi
it has hitherto been carried out, it presupposes the force-func-
tion unaltered in form with the variation of the motion, while
such an alteration of form is sometimes essential in physical
considerations. This is the case, for instance, with the mole-
cular motions designated as heat, as soon as the bodies are sub-
jected to changes of volume and pressure. In regard to the
quantities accentuated especially by Clausius, which occur toge-
ther with the coordinates in the force-function, and vary with
the variation of the motion, while they remain constant within a
given motion, it was therefore needful that the method should
be amplified ; and this has led to a somewhat more general form
of the equations of motion.
§1.
Given a system of n material points reciprocally attracting and
Digitized by VjOOQ IC
ruuUingfrom Hamilton's Theory of Motion. 370
repelling, but subject to no other forces, so that the soliciting
forces can be represented by the negative partial differential
quotients of a fnnction of the coordinates of all the points, the
force*function U. This function contains as variable quantities
at all events the coordinates g^ of the points in motion, of which
it is here always presupposed that thev identically satisfy at any
moment the eouatious of condition, of whatever form> and there-
fore, if m sucn equations are given, occur to the number of
8n-*mr;i/i. Moreover the time / may appear explicitly in the
force-function, as well as other quantities Ck, which change only
when a transition takes place from one motion to another. For
motions of this general sort, Hamilton's method for gaining the
general symbolical equation of motion which refers to the varia-
tion of the motion is to be extended. If the via viva of the
point-system be denoted by T, and the primary function Y Re-
fined by
-"-!>-
V)dl,
the problem is nearer to that of finding the variation of this inte-
gral on the hypotheses made.
In forming this variation, the time / is fii'st regarded as an
independent variable which is not variated. All the quantities
present in the primaiv function are therefore regarded as func-
tions of/ and a number of arbitrary constants; and from the
variation of these constants alone will the variation of those
quantities, and hence that of the primary function, result. Of
such arbitrary quantities there will always be 2/jl in the quantities
mentioned, which can be supposed to arise from the iutegration
of the /A differential equations of the second order of the motion ;
but since a variation of the force-function on the transition from
one motion to another is presupposed, to those 2/i constants any
number of others may be added ; these latter, which at all events
are assumed to be independent of one another, are the quantities
c^ If, then, these 2/i+v constants change, but / be supposed
unchanged, we obtain
-8V=Sr(T-U)rf/« rS(T-U)rf/,
Jo Jo
and we have only to do with the variation of the quantity (T-*U).
Since the equations of condition of the system may explicitly
contain the time t, the vis viva T will in general, as well as the
force-function U, likewise explicitly contain it; but since the
time is not variated, in the formation of the total variation 5V
Digitized by VjOOQIC
280 Prof. J. J. Muller on a Mechanical Principle
there occur only the variations 8y,, hq\, hcj^ and we have
By partial integration in the second part of the right-hand
side there hence results, if the values of the various quantities
for the time /=sO be denoted by the index 0,
and if we put the dtiferential quotients of the via viva, taken ac-
cording to y'p
according as they are referred to the time / or to the initial time
0, we get
This is an equation of motion of the most general kind, similar
to one to which prominence is given b^ Jacobi* and to another
by Scheringt ; but it has the peculiarity that the quantities r^,
not contained in the latter equations, occur in general in the
force- function likewise.
AH the quantities in equation (1) are presumed to be functions
of / and 2/i+v arbitrary constants, of which the first 2/i have
arisen from the integration of the differential equations of the
motion. The quantities y^, q\ can now, by means of the integral
equations, be expressed by the arbitrary constants and /; but
by the same integral equations the 2/i arbitrary constants can
also be represented by the quantities q^^ q^, and t. Let the latter
be presupposed. Then Y becomes a function of / and 2/jl quan-
titics q^, q^ ; but it contains in addition the arbitrary constants r^^
* Vorhsungen uber Dynamik, pp. 143, 356.
t HamiUon^Jaeobi'sche Theorie, p. 19.
Digitized by VjOOQ IC
resulting from Hamilton's Theory of Motion^ 281
which, in consequence of the supposition made^ are not connected
with one another by any relation. Hence all the variations
iq^, iq\f Bcj^ become mutually independent.
In consequence of this^ equation (1) can be immediately split
up into single equations. Puttings that is to say, the expression
which stands under the integral-symbol
^B-'-%=Ph"'-
we get the differential equations of the motion
dt "" ^g, '
and as, conversely, the latter are demonstrated by Lagrange to
be independent of equation (1), it follows that the expression
standing on the right-hand side under the integral-symbol va«
nishes under all circumstances. Therefore neglecting it, we
have
■8V=2i>^y,-2^:SgJ-£2|^M<J
(2)
and this is Hamilton's symbolic equation expanded. Because,
namely, the variations are all independent one of another, they
furnish at once the integral equations
Equation (2), with only an unimportant difference in the way of
writing it, has already been given by Clausius*; it is, however,
to be remarked that his deduction refers only to motions of which
the force-functions and equations of condition do not explicitly
contain the time. The form in which it gives the variation SV
is not su£Sciently general for the following considerations, because
in general the time t likewise varies, and therewith a partial
change is produced both in T and in U and consequently also in
V, which is neglected in equation (2).
It shall therefore now be assumed that the time t is no longer
the independent variable, but undergoes the change Bt on the
variation of the motion. In order to understand the sense of
this variation, it must be considered that the time is not to be
variated wherever it occurs, but only where it occurs explicitly ;
for a variation of the other would amount to a variation of the
initial and final coordinates ; and this is already done. In this
case, therefore, the primary function V is taken as dependent on
the initial and final coordinates, this explicit time /, and the
* Pogg. Ann, vol. cl. p. 122.
Digitized by VjOOQ IC
383 Fiof. J. J* MOUer an m MmAaniMi Prk^ctpk
qumtitias Cki tnd their Tariatkm it to be ftmnedb^Tiriatingdl
these qoantities timaltMieously. Hence the total variation formed
under inclusion of the time becomes
and the question is^ to determine the last term ^ •
In order to obtain this^ let it be remembered that, in the dif-
ferentiation according to i, the quantities e^ contained in the
force-function U have been supposed not to vary. From this it
follows that
and from thU we get immediateljr the partial differential quotient
•onght
If we introduce this value into the above equation for 8V, the
result is
-(U-T+2;>,9',)8/. . (3)
This general equation relative to the variation of motion, which
corresponds to the equations 7**^ aud 7a given by Lipschitz,
pp. 122, 138, as well as to Schering's equations [5] and [6],
p. 19, oontaining also the differential equations, is also valid, as
soon as a force-function exists, when the force-function and equa-
tions of condition explicitly contain the time. For the special case
which alone comes into consideration in the following, where the
time does not explicitly appear in the force-function and condi-
tions, it takes a somewhat simpler form.
That is, in this case the relation holds,
T+U=E,
if E denotes the energy of the system. Hence, if we add and
subtract, on the right-hand side of the equation for ^, the value
2T, we get
|^=E + 2;7,7,-2T.
But, with the hypotheses laid dowui the vis viva becomes a ho-
Digitized by VjOOQ IC
reiulttngjirmn Uamilton't Theory of Motion. 283
mogemaoos fanction of the second d^;Fee of the variable g'l ;
therefore
consequently we have simply
and after substitution in the above equation,
-SV=Sp,Sy,-2pjSffJ-r2|^5c*rf/-E8<. . . (4)
This form, connecting itself with Hamilton's equation*^ is the
starting-point for the following. At the same time it is signifi*.
cant that the ordinary equations of motion of Lagrange are re-
garded as satisfied only in the motion itself, and not during the
change of motion. The system must therefore, in the motion,
always be a closed one, subject to no action from without ; on
the contrary, during the variation of motion such an action from
without must take place. Meanwhile the energy of the system
may remain constant or vary ; whether the one or the other, has
no influence on the validity of equation (4). This independence
of Hamilton's equation upon the nature of the variation of the
motion has the same signification as that of Lagrange's equation
of motion upon the nature of the variation of the configuration »
If, therefore, Lagrange's method reaches to systems with and
without conditions, Hamilton's equation (4) extends to systems
which with the alteration of their motion retain the energy con-
stant or even receive energy from without.
§2.
Hamilton's symbolic equation of motion plays in the treat-
ment of the mechanical problem a part like that of the symbolic
equation of motion of Lagrange, only with the difference that it
refers to the variation of the motion, while the latter concerns
the variation of the configuration in a motion. If, now, in La-
grange's method from the equation of motion a series of princi-
ples result which have partly the purely analytical signification
of integrals of the differential equations, ana partly the essen-
tially physical meaning of general propositions valid for motion
generally, the question arises whether similar principles do not
connect themselves with Hamilton's equation. This shall be
investigated especially in regard to the proposition concerning
• Phil. Tnuis. 1884, p. 30/.
Digitized by VjOOQ IC
284 Prof. J. J, Muller on a Mechanical Princgfle
the vii viva, which has acquired by far the greatest importance
in Lagrange's method.
For that purpose, the already indicated presupposition is made,
that in all motions henceforward to be examined time does not
occur explicitly, either in the force-function or in the equations
of condition ; so that Hamilton's equation takes the form
-SV=2;?,Sy,-2pJS}J-f 2|5^M^-E«/, ... (4)
Jo ^^k
Making use of the well-known substitution given by Euler^ and
employed also by Hamilton and Jacobi^,
V=-W-fE^,
from which
SV=-8W+ES/ + /8B,
this equation of motion changes into
Herem
SW^:Ep^q,-lp^hq^-C^^Scf^t + tSE (5)
n
W=-V+E/=r(T-U)rf/+(T+U)/=r(T-.U)rf/
Jt Jo
and is therefore nothing else but the quantity known under the
name of the expenditure of force. It is to be understood as a
function of the quantities q^, q^, E, c^ ; and the time t, which in
the integral in equation (5) remained over, is to be replaced by
the equation
so that / and E in equations (4) and (5) occupy a perfectly ana-
logous position, in such sort that the one quantity may always
replace the other. If now the two relations (4) and (5) be com*
pared, there comes
In this equation the variations are still quite undetermined.
One of the infinitely many systems of virtual variations will now,
under the suppositions made, be the system of the variations
which enter with the actual change of motion during the minute
portion of time dt. Referred, however, to these actual variationsi
* Compare the general transformations of Lipscbitz and Schering.
Digitized by VjOOQ IC
resulting from Hamilton's Theory of Motion. 285
it makes
ind the second and third terms in equation (6) can each/ in rela*
tion to the coordinates, be conceived as an explicit alteration
according to / which may be expressed by
ilA
Then comes
ffljm_[B<^]=„, . . . „
and this is the proposition sought: The sum of the alterations
in the primary function and the force^ea^nditure, which are pro*
duced by the variation of the initial and final coordinates alone, is,
in the variation of every motion that presupposes a force-function
and neither contains the time explicitly in this nor in the conditions,
equal to nil.
As the variation of the motion is only subject to the condition
that it does not destroy the limitations of the system, but in the
rest, as already shown, may very well take place under accession
of energy, the proposition we have gained is independent of the
special kind of the accession. In this relation the coordination
with the proposition of the vis viva, which likewise gives the in-
crease of the latter independent of the kind of variation of the con«
figuration, is evident. But this independence forms only one side
in the latter proposition ; it has received, as is known, another,
more important, through the remark that the force-function (in
the above representation) is nothing else but the potential energy
of the system. In such a new direction the new proposition
shall now be investigated.
The sought signification of the primarv function readily ap*
pears if we give up the forces on which the ordinary theory of
motion rests, and introduce in their place momentary impiuses
capable of producing the velocity existing at any instant. That
such a manner of consideration stands in essential connexion
with Hamilton's theory of motion has not yet, so far as I know,
been rendered evident, although Thomson and Tait have recently*
drawn attention to the importance of this second method of pro-
cedure, not inferior to the first, and have more nearly completed
its theory. In it the components of the momentary impulse
(formed according to the general coordinates), if the components
of the forces taken according to the rectangular coordinates be
♦ TreatiBe on Natural Philosophy, pp. 206 et seqq.
Digitized by VjOOQ IC
686 Prof. J. J. Miiller on a Mechanical Principle
XYZ, are
On the other hand, if tf and v denote the componenta (formed
aeoording to the coordinate qt) of the velocity before and after
the impulse Pf, the meohanioal work done by the forces during
the impulse is
L-P,^-.
If now a system of /i impulse-components Pj be presuppoaed^
which shall bring forth the whole of the velocities ^t from the
state of rest of the system, so that the velocities prec^ng them
are all kO, but the velocities after them those 70 then the me-
chanical work done by the forces during the impulse becomes
But the equivalent vi$ viva
therefore
and
-sl-'.^ <•'
that iS| the negative partial differential quotients of the primary
function, formed according to the coordinates, represent the
components of the momentary impulse which is capable of bring*
ing about the velocity existing at the time in question.
If, from («), the vdue of P| be inserted in
af
there results further
and
-x^dg,=2hdt} m
that is, the negative partial differential of the primary function,
formed according to the whole of the coordinates, represents the
Sroduct of the time- element dt into twice the mechanical work
one by the impulses which bring forth from the state of rest
the actual velocities q'i.
If, finally, the value of this partial differential, from (fi), be
Digitized by VjOOQ IC
rmdiing from Hamilton's Tkem) of Motion. £87
introdaoed into the equation
we get
and from this.
V=J'(E-2L)rf/, (y)
a relation which is immediately obtained from the earlier defini*
tion-eqoation of V by making use of the proposition of the
energy, was used by Hamilton without hesitation as a definition
of the function Y, and expresses the proper mechanical meaning
of the primary function.
As, then, in (7) the primary function appears to be formed
analogous to the earlier quantity W, it will be convenient to in-
dicate this by a similar notation ; and the names of potential
and kinetic action may commend themselves for Y and W. If
we put, moreover,
A«V+W=E/,
and name this simply the action of the system, equation (7)
changes into
#-[|^].o. ...... <e,
and the proposition reads : — That alteration of the action which
is conditioned by the variation of the initial' and final coordinata
alone, vanishes with the change of every motion that presupposes a
force-function and does not contain the time escplicitly either in this
or in the limitations. In this form it may be designated as the
principle of the action.
Here {^ential and kinetic action are quantities characterizing
the given motion in like manner as the potential and kinetic
energy the corresponding configuration* If we imagine the
whole series of constantly altered motions to be run through,
they will in general be distinguished by different values of these
Suantities : in proportion as, by the mere alteration of the coor*
inates, the one diminishes, the other increases through the
same alteration; so that in this new view perfect correspondence
exists with the proposition of the energy.
In regard to the limitations under which the proposition of
the action has been obtained, it is to be remarked that the for-
mation of 1 2Tdt, like that of T, remains possible even without
a force-function. Now the question, what in these cases becomes
Digitized by VjOOQ IC
288 Prof. J. J. MuUer on a Mechanical Prineipk
of the proposition of the action when there is no force-fanction,
and consequently no primary function^ gives occasion to bring
oat its position to another well-known equation in medianicSy
which relates to the above-mentioned momentary impulses.
If, namely, the components of the impulses, formed according
to the axes of the rectangular coordinates, are BHZ, and the ve-
locity-components induced by them are s^y'sf, the equation of
motioA i?
2[{a-iiwp')&r+(H-my08y+ (Z-»»^S^] =0.
If now as a system of virtual variations the actual alterations of
the coordinates be introduced, there results
Integrated over the given motion, there comes
Und from this results, by variation.
(9)
This is the equation which, in the general case assumed, takes
the place of the action-equation ; its terms have a similar mecha-
liicu meaning to that of the terms of the latter. That is to say,
the sum of the left-hand side is nothing else but twice the me-
chanical work which the sum of the forces constituting an im-
pulse perform during the same. The equation, therefore, imme-
diately passes into
' 'iTdt; (10)
B('2Ldt=s('
Jo Jo
and the action-proposition also can be easily brought into this
form; for, according to (7),
which, inserted in its equation, furnishes immediately the form
(10) . The difference between the two cases consists only in this,
that in the case of a force-function the terms of the equation are
functions of the coordinates, in the other case they are not so —
relations analogous to which occur likewise with the proposition
of the energy.
§3.
In order to illustrate the principle found, which represents a
characteristic property of the variations of motion of all systems
which satisfy the oft-insisted-on conditions, a simple example,
Digitized by VjOOQ IC
resuliinfffrom Hamilton's Theory of. Motion. . 289
for which the propoution can readily be verified, may first be
discussed. For tnis I select the motion of a pendulum which
takes place in the vertical plane of xy about the downward-
directed axis of the positive y in infinitely small amplitudes; and
I give the determination of the two functions V and W accord-
ing to known methods''^.
The length of the pendulum being denoted by /, and the elon-
gation each time by 9^ so that
x^lwOiOy y^lcoH0,
the energy E expressed by the quantities Pi and q^ becomes
B = i^-^/C08tf,
where ps^-». Accordingly the differential equations of the
motion are^ taking account of the infinitely small amplitude,
d0_p
and the two integral equations
where 0q and|>o denote the values of 0 and/? for /=0.
Introducing now these values into the expression for the vis
viva
and substituting for the squares and products of the trigonome-
trical functions the doubled variables, we get
-¥'\/?"°»\/?'-
* Compare Hamilton's and Jacobi's examples.
PhiL Mag. S. 4. Vol. 48. No. 818. Oct. 1874. U
Digitized by VjOOQ IC
SgO Prof. J. J. Mailer on • Mtiktamtl Pvituirle
When theMunevilaesaK alao introdooed into the fiHce-fiiactian
there remiUe, aftar a eimikr redoetioo,
and inserting, finally, both these values m the primary fonetion
-V-fcT-U)*,
we obtain
or^ if by aid of the first of the integral equations we put
and, lastly, introdnce again into the trigonometrical fonctions the
simple variables^
-\:r.gU + i{0' + 0tily/7li>OtAyp—^Sllb^. (11)
Referred to the same variables / and 0, we have on the othor
hand
If this, together with the value of U, be inserted in the known
differential equation for A,
T«-U+E,
Digitized by VjOOQ IC
remUmg from Hantilton's Theory of Motion, 291
die retttU is
and from tbu the integral
W-JV2i^/»+2/«E-^/»fl«i^. . . (12)
If we now form out of (11) and (12) the differential quotients
Jt nn^i;
dW
dd,
= -V'2^/»+2/«E-^/»^,
and introduce them into the action-equation, we get
d8.
-s/Zgl»-\-2m~gl»0l-^
'• • •
(18)
Indeed it ean be readily shown that the indiyidaal derivata
are p and p^ respectively. For if the quantity p^ be eliminated
from the second of the integral equations for example by aid of
the first, we get immediately
tanA/^/ sin-v/l^
'^e
and if we put this value of /> in the expression of the energy, it
changes into
E=
ir/«^cos«y^^^2y/WoC08^|/+^/^^
2/«sin
and hence
\7f
-'(-f)»
aw
/ gl'0*coH*^it-2gPB0oCOBAy'
V tin* A /it
U2
^jt+gl^e\
-=/».
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29.2 Prof. J. J. Miiller on a Meehamcal Principle
Of the applications of the proposition of the action^ those shall
be introduced here which can be made of it in the mechanical
theory of heat. If heat be conceived as molecalar motion, the
application to it of the Ener^ proposition leads immediately to
the first main proposition of this doctrine. Corresponding to
this, we are now mvestigating what, on the same hypoth^ia,
resalts from the Action theorem. These molecular actions are
stationary motions of a system of points ; and the simplest case
of such motions is obviously that in which all the points move
in closed paths, and with a period common to all of them. TUs
shall first be supposed.
As, for closed paths, the two limits of the integral which
forms the action coincide, when the integration is extended over
an entire revolution we obtain
m of the Action propi
and hence the equation of the Action proposition is transformed
into
or, written explicitly,
QCj^
If now, for one revolution, we name the mean value of the mt
viva T, and that of the force-function U, we obtain
-y.j;(,-,
-U)A=/(T-U),
-<rsr=/iT-/iu+f*-tJ<ft,
E=T+'U;
and if we insert this value in the above equation, we obtain
from which
dU-.2|^&^=i?T+21Wlog/, . . . (14)
a well-known equation, already advanced by Clausius'*' for audi
motions.
If now we apply this or related equations to the molecular
♦ Pogg. Ann. vol. cxUi. p. 433. Phil. Mag. S. 4. vol. xlii. p. 161.
Digitized by VjOOQ IC
resulting from Uamiltoii^s Theorjf of Motion. 293
motion designated heat, making use at the same time of the hy-
pothesis that the temperature is proportional to the vis viva of
the motion, we arrive (as Boltzmaun, Clausius, and Ledieu have
shown) easily at the second proposition of the mechanical theory
of heat. In general, however, the motion of the molecules of a
body does not take place in closed paths. With respect to fluids,
for example, we are not even justiiSed in assuming for them a
fixed mean position ; and in the case of solids, where such an
assumption is indeed necessary, the actual motion will yet be
distributed along all the dimensions. Now, for such cases Clau-
sius has recently called attention to a second, analogous equation,
which substitutes another hypothesis for that of closed paths.
A more direct derivation of the second main proposition from
the theorem of the action shall here be given.
The suppositions which have been made respecting the system
of pNoints representing the body are simply that the motion is a
stationary one, and t^^t it is infinitesimally changed by the com-
munication of an elementary quantity of heat. The subject of
investigation is the quantity
which refers to the variation mentioned. Since infinitesimal
alterations of the velocities in the time-particle dt produce only
infinitesimal path-changes of the second order, this makes
Further, the system of variations -^ can be split into two.
Let the first be the distances qidt which are traversed in the ori-
ginal motion during the time-element dt from the points q^,
Iliis portion furnishes the sum
Let the second partial system be the distances Cidt which lead
from the above-mentioned last positions in the original motion
to the final positions in the changed motion. In it, under the
suppositions made, to every value o{p there come just as many
positive as negative e; this portion therefore furnishes the sum
Accordingly, for the infinitesimal variation which in the sta-
tionary motion of the point-system is conditioned by an infinitely
small quantity of heat.
Digitized by VjOOQ IC
294 APrimiipkrenMiiffJhmEmaSiUm'tTkimytfMttiom.
Ilierefore, introdaeiDg th« fanetion "V,
and the equation of the aeiton ean be written
But since
we have
dVr^2tdf+2fdt,
and from this
rfE-2 |^ifc*=JWT+2'rrflog/,
or
^E-2||^,=2TJlog(/T) (15)
Now this equation, which has already been given by Siily*
for the special case in which no Ck are present, the paths arc
closed, and the periods are the same for all the points, leads im-
mediately to the second proposition of the mechanical theory of
•?*Lr • . ^ **^** purpose let us consider, first, that the left-hand
side of It IS nothing else but the energy which, with the ehange of
the molecular motion, is communicated to the body as heat from
without ; and therefore, in the usual noUtion of the theory of heat,
it is J rfQ. If we then make use of the assumption that f is
proportional to the absolute temperature 8, we immediatel/
■8=^' (16)
understanding by dS a complete differential.
Thus the Second Proposition is derived, like the First, from
a general mechanical principle. But the above representatiofi
permits us to perceive for the two propositions not merely this
♦ Pogg. Ann. vol. cxlv. p. 295. Phil. Mag. S. 4. vpl. xliii. p. 339.
Digitized by VjOOQ IC
Mr. J. CVKuMtly onMNewFommU in Definite Int^als. 206
confortnihr of position, bat d80 a eommon origin. Tho derelop-
ment of the variation of Hamilton's integral bias the peeoliarity
that it leads simultaneously to the differential and integral equa-
tions of mechanieal problems. This remarkable &ct gives to
the principles of Energy and Action a common origin in the
general equation of motion ; and by this the latter b^mes the
connecting band foi^ the two propositions of the mechanical
theory of heat.
Zurich, April 1874.
XLI. On « New Formula in Definite Integrals.
To the Editors of the Philosophical Magazine and Journal.
11 Elysium Row, Calcutta,
6BNTLBMBN3 Augurt 2, 1874.
I SEE in the July Number of your Magazine two new for-
muln in definite integrals of some importance are given by
Mr. Glaisher. The integrals admit of a direct general solution
without using the identity on the right-hand side of the equa-
tiouj
^o-«i^+««^&c. = x^, - (r^t^-
The portion to the left is evidently equal to
1
or putting Es=€^*,
From this
I
And taking the limits n and 0^ the value for this particular ease
is
E_i IT IT
2 * ^"* 2 ' ^''*'
The second theorem is obtainable in the same way. It is
udx
i+^.(l+B««)'*^
=(1-E)-'. {tan-'x-E*tan-'E**}<^,.
Digitized by VjOOQIC
296 Mr. F. Guthrie on an Absolute Gatponometer.
This is the general solation ; and where the limits are infinity
and cipher^ there results
(l-E)-'.J.{l-e-i}ao=|.{l+E»}-'*o.
whieh is the same as given by Mr. Glaisher.
It is evident that there are numerous theorems of the same
kind, such as
cos Ej? . flo=flo~ 1^ + *^v
sinEa?.flro=«i*.- 123**^-'
which will give definite results between the limits infinity and
cipher.
Yours obediently.
Jams O^Kinealt, B.CS.
XLII. On an Absolute Galvanometer.
By Frederick Guthrie *.
MESSRS. ELLIOTT have constructed for me a galvano-
meter which willy I believe, be found to possess for some
purposes certain advantages over those at present in use. Its
Erinciple depends upon the measurement of the current-strength
y the measurement of the mechanical force necessary to bring
toa given distance of one another two electromagnets, which
are excited by the current in such a fashion that they repel one
another.
The current'enters at a by the screw-damp ; thence it passes
beneath the circular wooden stand C along the copper wire mb.
It rises vertically and coils round a soft iron mass/, which lies
horizontal and tangential to the axis of the instrument. It
passes down And across the centre of the board, then rises and
coils round a soft iron mass /', exactly similar and similarly
placed to/, but on the opposite side of the instrument. Having
encircled/', the current- bearing wire again descends, and carries
a mercury- cup y, through whose bottom it passes, and which is
exactly in the axis of the instrument. The current then leaves
the mercury by the wire t, which dips into it. It then traverses
the wire around the iron, m. Thence it crosses the instrument
and forms a spiral around m!, after which it passes into the mer-
cury-cup A, and so to the binding-screw c. The spirals are such
* Read before the Physical Society, May 23^ 1874. Communicated by
the Society.
Digitized by VjOOQ IC
Mr. F. Guthrie em mAb$obUe Galvanometer. 297
that there is repulsion between /and m, and also between m! and
/'. It is seen that the magnetic pair//' is fixed. The pair
m m! is movable about a vertical axis. The system mm' is hung
by a metal or glass thread k from the rod l, which works stif9y
through the nut o. The latter carries an arm and vernier, p,
which slides over the graduated head, q. The scale, nut, &c.
Digitized by VjOOQ IC
398 Ai9/jc«t rup$eiins New Booh.
are tnpported on the glass tabe r^ whieh is fastened by the sap t
cm to the plate-glass disk t, which rests upon the tap of we
!;las8 cylinder u clamped upon the wooden base e resting on
evelling-screws. In the side of v is a plate-glass window, w^
through which a vertical line of light may be focused upon x (a
mirror fastened to the mrrl system), and thence thrown upon a
scale in the manner which is now so often employed.
A word or two about the way in which the instrument is used.
The upper plate / and the system m mf are removed by lifting r.
The edge of u is rubbed with beeswax to prevent t from slipping
upon it. The copper wires penetrating the cups are amalgamated
and a little mercury poured in. Amalgamated thin platinum-
foil is then pressed into the cups, and mercury is poured upon
this. By this means a concave meniscus is obtamed. The upper
partis then replaced, and so adjusted by turning the plate / and
the cylinder u that the mirror x is parallel to the window v,
when the axis of m ni makes an angle of about 15^ with that
oiff. The rod / is adjusted so that the wires of m mf just touch
the mercury ; and by the leveUing-screws A is so swung that m
and^ and ako ni and/', are exactly opposite to one another and
the wires in the centres of the mercury-cups. A slit of light is
then sent through w, reflected on to a screen, and the head o is
then turned till the slit is split bv an arbitrary vertical line on
the screen. The reading of /> is then noted. A current passing
through the system forces mwl away from//'. Turn the head
0 untu the slit of light is again brought to the mark on the screen.
The angle through which it must be turned is directly propor-
tional to the magneto-repulsion — that is, to the square of the
current-strength. Many of the laws of electrodynamics may be
readily illustrated by this instrument; and not only may differ-
ent currents be compared with the greatest accuracy, but the
absolute mechanical magneto-value of the current may be at
once arrived at. By bringing the repellent magnets alwaj's to
the same distance from one another, a whole class of sources of
error is removed.
XLIII. Notices respecting New Booh.
First Lessons in Theoretical Mechanics. By (he Eev. Johh F.
Twisnm, MJL, Professor of Mathematics in the Staff CoUege,
and formerly Scholar of Trtnity College^ Cambridge, London :
Longmans, Oreen and Co. 1874: pp. 243.
npHOSE teachers and students who are already acquamted wi^
-L t^e author's large Treatise on Medianics, will naturally ex*
peot to^find in the work bow before us perfect exuct^ude both ia
Digitized by VjOOQ IC
Notices rstpesting New Booh. 309
and esqpreseion; nor will ther, making due allowanoe
for the cOflELculty of the undertaking, be m any way diflappointed.
It is^ not an easy task to teaoh eyen the first principles of me-
chanics to those of whom only a knowledge of jtnthmetic, a little
Geometry, a few rules of Mensuration, an aptitude in the use of
compasses, scale, and protractor, and enough Algebra to solye a
simple equatioa are demanded. Tet the author has performed
this task in a manner which shows that with him teaching is an
art of which he is an accomplished master. It is true tmkt now
and then he is obliged to omit or postpone the proofs of certain
important theorems which inyolye a knowledge of GFeometry and
Trigonometry not possessed by beginners. In the parallelo-
ri of forces (art. 37), for instance, the student is told to find
resultant by consianiction. That the resultant is the diagonal
of a parallelogram of which the two giyen forces are adjacent sides,
is assumed to be true — ^the reason of the rule being giyen in a sub-
sequent cluster (137), to which, howeyer, no clue is ^yen. And
this seems a suitable place, in our notice of Mr. Twisden's book,
for remarking that a work containing so much matter (&r more
than at first sight appears) ought cer^inly to be furnished with a
copious index.
That the centre of Rrayitjr of a triangle is the intersection of the
three straight lines which join the yerfcices to the middle points
of the opposite sides, is a proposition also giyen without proof
(art. 18), showinff that the litue Geometry which Mr. Twisden
requires of his readers does not eyen extend to the proof of so simple
a theorem. In art. 18 (6) we are told that <' any area may be
conceiyed to be made up of a number of parallel straight lines,"
a conception which mujst be inconsistent with the youmy; geo-
meter's notion of a straight line. By use of the principle of limits
in finding the centre of grayity of the surface of a triangle, this
inconsistency would certamly be ayoided.
The book consists of eight chapters, the first fiye of which are
made as simple as possible. Each chapter is followed by a collec-
tion of excellent questions, not less than foor hundred altbgether
being giyen in this manner. Besides, nearly two hundred complete
solutions of useful and interesting problems are scattered through-
out the book, inyaluable to those who study without a teadier.
There are also Tables of Specific Grayities, Moduli of Elasticity,
Tenacities, and Besistances to Compressions.
We rec(Hnmend the book to the notice of that numerous class
for whom it is speciaUy intended — ^those who must know mechanics
and yet possess out little mathematical knowledge — to Students, as
beinff suitable to the curriculum of the TJniyersity of London, and
to all Teachers, on account of the always clear, ana often ingeniousi
deyelopments of the most important parte of the subject.
Digitized by VjOOQ IC
800 Notice* respecting New Booh.
Supplement to the First Book of Euclid's Elements, eontaininff ihe
Sixth-Book Propositions proved independently of the Fifth Book^
and the Elementary Propositions of Modem Geometry, By "Edward
Botleb, M.A.T.C.D. Dublin : Alejomder Thorn. 1872 (12mo,
pp. 60).
Euclidian Geometry. By Fbakcis Cuthbebtsok, MJL, late Fellow
of Corpus C?iristi CoUege, Cambridge, Head Mathematical Master
of the City of London School. LondQa : Mftcmillm and Co*
1874 (fcap. 8yo, pp. 266).
The titlepages of these works suffidentlj indicate their pur-
pose ; they are intended to be substitutes for Euclid's G^eomet^T,
or for nart of it, and while retaining the form and spirit of the
original, to improve on it in detail and to supplement its supposed
deficiencies. Both books are, to all appearance, written hj madie-
matidans of average competency ; and one, at least, of the authors
(Mr. Cuthbertson) is in a position which makes it highly probable
that he is a teacher of considerable experience*. But though this
is the case, we regret to have to add that, after having looked into
these books with some care, we do not see why they have been pub-
lished.
With Mr. Butler's book the difficulty is not so great as with
Mr. Cuthbertson's. We may surmise that it is adapted to s<Mne
course of instruction sanctioned by the Commissioners of National
Education in Ireland ; and if so, its somewhat fragmentary form is
explained. It consists of a number of propositions designed as a
substitute for Euclid*s sixth book, and a selection of elementary
propositions on Harmonic and Anharmonic Section and some allied
subjects. It is hardly necessary to notice this book further ; and
were we asked for the reason, we should regard it as a sufficient
answer to state that Mr. Butler's definition of proportion runs
thus : — " Four straight lines are said to be proportionals, that is,
the same ratio the first to the second as the third to the fourth,
when the rectangle contained by the first and fourth is equal to
the rectangle contained by the second and third." Putting out oi
the question the typographical error which may be presumed to
exist in the passage, the sentence betrays a view of the functi<m
of definition which is above or below criticism.
Mr. Cuthbertson's book covers just the same ground as Euclid*8
Books 1-6, and the first twenty-one propositions of Book 11. He
has manifestly expended a great deal of care and thought on its
composition, and yet we are constrained to say that his attempt
to improve on Euclid is a failure. In the first place, his book is
about as Ions; and quite as abstruse as Euclid's. In the next, he
has increased the difficulty of his task by adapting his book to a
certain form of examination which our limits will not allow us to
* We do not know what position Mr. Butler holds ; he calb himself *' Pro-
fessor Ao. under the CommissionerB of National Eduoation in IreUnd." We
are wholly in the dark aa to the meaning of the *' Ac."
Digitized by VjOOQ IC
Notices rapecting New Booh. 801
explain. Then, again, the substance o£ his book seems to us of a
far inf eri(»r qui^tj to Euclid's : this is no more than might be ex-
pected; but we will giye an instance of what we mean. Euclid's
treatment of the Corollaries to the 32nd prop, of Book 1 is not, per-
haps, wholly proof against minute criticism ; still i£ any thing be
wanting it could be supplied by a word or two of explanation ;
and surely nothing can be plainer or more direct than his method.
Mr. Cuthbertson, however, wishes to improye upon it, and he does
so as follows: — On p. 39 he gives a Corollary, which is stated
thus : — " If A B, B C are two straight lines respectiyely parallel to
DE, EF,then shall the angle ABCbe equal to the angleDEF."
This is traie or not according to the direction in which E F is drawn :
e. g, it is true in the case shown in Mr. Cuthbertson's diagram ;
but the needful qualification is not given in^the Corollary, nor, so
&r as we have noticed, anywhere else. On p. 48 this Corollary is
used to prove the theorem *' if the sides of a polygon be produced
in order, the exterior angles shall together be equal to four right
angles." The proof consists in taking a point outride the polygon and
drawing from it rays parallel to sides respectively. This proof, of
course, may be made perfectly sound ; but in the case before us it
fails owing to the above-mentioned ambiguity. This is the way in
which he treats Euclid's second Corollary, and then he goes on to
prove Euclid's first Corollary. The method is in no respect better
than Euclid, and the way of stating it inferior to the extent of in-
accuracy.
There is one question of general interest, suggested by a perusal
of Mr. Cuthbertson's book, on which we will say a few woi^s, viz.
"What are axioms?" Td the mathematician they are merely
truths of geometry assumed without proof, as premises needful for
proving other truths of geometry. It is usual to answer that
axioms are self-evident truths. But, not to say that the question at
oAce arises " Self-evident to whom ? " it is to be observed that the
question " How do we come by our knowledge of the axioms of
geometry ? " is one with which the mathematiGian, as such, has
nothing to do. There are, of course, two distinct ways of answering
this question, and each doubtless capable of numerous modifications.
Some hold that the axioms of geometry are what they are in virtue
of the conformation of the mind antecedently to all experience of
space. Others hold that the axioms are nothing but the expression
of our most elementary experiences of space, and that what is
called their necessary truth is merely a consequence of the uni-
formity of our experiences, joined to the absence of any experience
which suggests so much as a type of something inconsistent with
them. "We believe this to be a sufficiently correct, though brief,
stl^ment of the two rival answers ; and the observation we have
to make on them is, that whether either or neither of them be true
is a question wholly outside of geometry.
We may not, perhaps, be justified in doing more than suspecting
(but at all events we do very strongly suspect) that the reason of
Euclid's 12th axiom being so much objected to is that many mathe-
Digitized by VjOOQ IC
302 Noiicei retp^iing New Booh.
maticiaiiB renrd tha former m ihe correct answer to the abora
question. There is not much difficulty in bebeving that we are
bom into the world with minds so constituted that as soon as wo
know the meaning of words we cannot do otherwise than hold that
things equal to the same thing are equal to one another; hdt na
one except a hardened metaphysician could suiq[K)se that a belief of
the 12th axiom is produced by any thin^ but an acgnaintmoe witii
the actaal properties ot space. Accordmgly many wish to substir
tute for it something which is more " self-eyident," «. s. something
more consonant with their metaphysical views.
It is not easy to see, on other grounds, what adTantage is ffi*^
by substituting; <me axiom tor another. No (me has any dimcoli^
inunderstandmg what the 12th axiom means, nor in seeing that it
is undoubtedly true. If any one will proye the conTerse of pro*
position 27 without assuming more than the first eleyen axioms
and the first 27 propositions, he will do something worthy of all
honour. But when the question is to proye the point by means oi
a special axiom which oi&rs from Sudid*s our interest in tha
matter is but small, e. g. U any one prefers Playfair^s azioBi to
Euclid's we do not know why he should not; only we would remaik
that it is merely a question of preference, that tiie two asdoms an
quite coordinate with each other, and that if either is taken £or
granted the other can be immediately proyed.
Mr. Cuthbertson, however, takes a oifEerent view from this, and
he goes to work to imnrove upon Euclid as follows : — On p. 83 ha
gives ** Deduction G-, vis, " If points be taken along one of iho
arms of an angle &rther and further &om the vert^ their dia»
tances [meaning, as explained, perpendicular distances] from the
other arm will at length be greater than any given straight
line.'' It is obvious that this statement as it stands is not tme;
however, the needful correction could be supplied wiihont mneh
difficul^; #• g. it would be sufficient for present purposes fiir it to
run, '* If points be taken at equal distances ^^ and this is wpfOr
rently what is meant. Further, the demonstration of the dedootoi
assumes that any angle however small can be multiplied until an
angle is obtained greater than a right angle. We have no objeotioB
to t^ being assumed, onl^ to its being assumed implicitly. In a
book which f ormaUy specifies the axioms assumed, it ought to
have been separately enunciated as an axiom ; and we canned find
that this has been done. On p. 34 Mr. Cuthbertson g^ves the
axiom which he proposes to substitute for Eudid's 12th axiom, vis.
" If one straight Ime be drawn in the same plane as another it
cannot first recede from and then approach to the other, neither
can it first approach to and then recede from the other on Hie sama
side of it.*^ By means of this axiom and deduction G, he succeeds
in proving Playfair's axiom. In other words (putting accidental
detects out of the question), he succeeds in proving one axiom by
assuming two. We willingly accord to this the praise of inpraiuity ;
but we strongly suspect that few besides the author will thmk it an
improvement on Euclid's method.
Digitized by VjOOQ IC
Royal Society. 808
We had marked for notiee our author's way of treating the
subject of proportion; but our limits will not allow us to fulfil our
intention. We will only saj that it seems to us a feasible way of
treating the subject (in the same manner as his treatment of paral-
lels is feasible^ but as to its being an improyement on Euclid's
method, that is quite another matter.
XLIV. Proceedings of Learned Societies.
KOTAL 80CIBTT.
[Continiied firom p. 226.]
Feb. 26, 1874.— Joseph Dalton Hoc^r, C.B., President, in the
Chair.
'T^HB following communications were read : —
-^ "Note on Displacement of the Solar Spectrum." By J. H.
N. Hennessey, rjt.A.S.
The following experiments were made with the (new) spectro-
scope (three prisms) of the Boysd Society, to ascertain for uds in-
strument the amount of displacement in the solar spectrum from
chanjB;e of temperature. The spectroscope was set up on a pillar
withm a small tent at a time ot the year when ike thermal range
is considerable : the cdlimator was placed horizontal, and directed
through a window in i^e tent to a heliostat, which was made to
reflect the sun's image when required. On closing the window
darkness preyailed in the tent, so that the bright sodium linea
were easily obtained from a spirit-lamp. Before commencing, the
slit was adiusted and the spectroscope clamped ; and no moy^nent
of any kind was permitted in the instrument during the experi-
ments. The displacement was measured by means of a micrometw
in the eye-end of the telescope, readings being taken (out of curio-
sity) successiyely to both dark and bright lines, i. «. to K 1002*8= Dr
and K 1006*8 sDtr A yerifi^ed thermometer was suspended directly
oyer and almost touching the prisms. The meteorological obser*
yatory referred to was some fiffy yards north of the tent.
Bejecting obseryation 5 (in the following Table) because the
thermomet^ was eyidently in adyance of the prisms, we deduce
By Dsrk lines, displacement equal g
Dr to Dt; is produced by ... . 31*3 change of t^nperature.
By Bright lines, displacement equal
Dr to Dt; is produced by. . . . 29*4 „
Mean.... 30
f nnn which it appears that the displacement in question may not
be neglected in inyestigations made under a considerable thermal
range.
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Mr. J.H.N. Hennessey on White Lines in Solar Spectrum. 805
" On White Lines in the Solar Spectrum." By J. H. N. Hen-
nessey, F.B.A.S.
Extract from a Letter jrom Mr, Hennessey to Professor Stokes.
" Mussoorie, Not. 12, 187a
*' My deab Snt, — Aa I cannot account for what is described and
drawn in enclosed, I hasten to place the same before you, intending
to look for the white lines in question so soon as I move down to
a lower altitude. Amongst others, no doubt KirchhofE closely ex-
amined the region in question, without notice of the lines ; and this
only adds to my perplexity, unless what I see here is due (1) to
altitude, or (2) is instrumental. In the latter case I cannot ac-
count for the absence of the white lines at Dehra, where I ex-
amined the spectrum generally several times ; I must, however, add
that without close examination and some experience, the lines
might easily be passed over. But if instrument^, to what are they
due ? I very much regret that the old spectroscope is not avail-
able at present [it had been temporarily sent elsewhere for a special
object] to enable me to verify the phenomena "
[In the drawing sent by Mr. Hennessey, the intervals between
the dark lines are coloured green, except in the place of the two
white lines. To transfer this distinction to a woodcut, an additional
horizontal band has been added below, in which only those parts
of the drawing which are left white appear as white, while in the
upper part the white of the woodcut represents the white or green,
as the case may be, of the original. — G-. G-. S.] -^
Part of Solar Spectrum, drawn to Kirchhoff*8 scaler observed at MuS"
sooric, N. W. Provinces, India, Lat. N. 30° 28', Long. E. 78° 4' ;
Height 6700 feet above sea (about^, toith the Spectroscope belonging
to t^ Hoyal Society.
Note for diagram. — In course of studying the solar spectrum for
atmospheric lines, with an excellent 3-prism (new) spectroscope
belonging to the Eoyal Society, I gradually exteiided my searcn,
PAi7. Mag. S. 4. Vol. 48. No. 818. Oct. 1874. X
Digitized by VjOOQ IC
806 RoifMlSomty;^
began at the red end, until on arriyal at theiedonabontt myatten-
tionL wm atta^acted by ilie faot tliat K 1657*1 Dy no meanB appeared
as the strong line depicted in Kirchhoffs map, Plate EL Cm ex-
amining tbis xegian oarefullj, I was surprised to find i^ oolimrless
lines shown in the diagram ; these lines, from want of a more ap-
propriate name, I shall call white lines (or spaces); they cannot ab-
solutely be described as bright lines, jet they doselr resemble
threads of white floss silk held in the light. The spec&oscope in
nse, witJi the most oonyenient hi^est-power eyepiece, presents
images of about two thirds to seyen nintlis of those drawn in the
diagrami the former are exa^rated by reckoning to agree with
Kirchhoffs millimetre scale; it will theiefore be readily understood
that the white lines do not present striking objects in the spectro-
scope, especially about the time of sunset, when I happened first
to notice them ; the^ are best seen about noon, when their resem-
blance to threads of white floss silk is very close ; but once sem,
the lines in question can always bereadily detected. So fiiras imr
instrumental means permit, the wider line extends between K
1657*1 and K 1658*3; more accurately speaking, it fiJls short of
the latter and rather underlies the former; the narrower white line
is underneath K 1650*3, sensibly more of the former appearing
beyond the edge towards yiolet of the latter, which presents the
quaint look of a blade Une on a white surface enclosed in a green
band. These are the only white lines in the speotirum from extreme
red to F; they are not bright (or reyersed Imes), so far as I haye
had opportumty to judse. Were they bri^t lines, the question
would arise, why these alone should be reyersed at 6700 feet aboye
sea. like the black lines the white lines grow dim and disappear
with the slit opened wide. As seen here, K 1657*1 is senmbly
weakw than K 1667'4, whereas KiiehhoS assigns 5 5 to the former
and only 3 a to the latter.
March 12. — JoBeph Dalton Hooker, C.B., President, in the CSiair.
The following communication was read s —
" On a New Deep-sea Thermomet^." By Henry Negretti and
Joseph Warren ISambra.
The Fellows of the Boyal Society are perfectly aware of the
assistance afforded by Her Majestys Ooyemment (at the request
oi the Bojal Society) for the purpose of deep-sea inyestigations,
and haye been made acquainted with their results by the Aeports
of those inyestigations published in the ' Proceedings of the Koyal
Society ' and by the interesting work of Professor WyyiUe Thom-
son. Among other subieots, mA of the temperature of the sea at
yarious depths, and on the bottom itself, ig dtike greatest import-
ance. The Fellows are also aware that for thb purpose a peculiar
thermometer was and is used, haying its bulb protected by an
, outer bolb or casing, in order that its indications may not be yiti-
ated by the pressure of the water at yarious depths, that piessure
being atx>ut 1 ton per square inch to every 800 fiithoms. This
Digitized by VjOOQ IC
Messrs. Negretti and Zambra on^^ De$j^$ea Thermometer. 807
tberounnetery as regards the protection of the bulb and its Hon-
lial^ty to be affecred hj pressure, is all that can be desired ; but
unf ortuiuktelj the onlj thermometer available for the purpose of
registering temperature and bringing those indications to the sur-
&ce is t^ which is oommonlj Known as the Six's thermometer
— an instrument acting by means of ^cohol and mercury, and
having movable indices with delicate springs of human hair tied to
thekn» This form of instrument registers both maximnm and mi»
nimnm temperatures ; and as an orfnary out-door thermometer it
is verj useful; but it is unsatisfactory for scientific purposes^
and for tiie object for which it is now used (viss, the determination
of deep-sea temperatures) it leaves much to be desired. Thus
the alcohol and mercury are liable to get mixed in travelling, or
even by merely holding the instrument in a horizontal positiim ;
. the inmces also are liable either to slip if too &ee, or to stick if
too tight. A sudden jerk or concussion will also cause the in-
strument to give erroneous reading bv lowering the indices, if
the bl«ir be downwards, or by raismg them, if toe blow be uth
wards. Besides these drawbacks, the Six's thermometer causes the
observar additional anxiety on the score of inaccuracy; for, although
we get a fnmimum temperature, we are bv no means sure of the
poiiS where this minimum lies. Thus nx)fessor Wyville Thomson
says ('Pepths of the Sea,' p. 139): — ^'^ The de»^rmination of tern-*
perature has hitherto rested chiefly upon the reg^straoon of mini-
mum tiiermometers, It is obvious that the temperature registered
by mmimum thermometers sunk to the bottom of the sea, even if
their registration were unaffected by the pressure, would only give
the lowest temperature reached Bcmewher^ between top and bottom,
not neutiarihf at the bottom itself. The temperatures at various
depths might indeed (provided they nowhere increased on goinf
deeper) be determined by a series of minimum thermometers placed
at mfferent distances luong the line^ though this would involve
considerable difficulties. Still, tiie^ liability of the index to slip,
and the probability that the indication of the thermometers would
be affected by the great pressure to which they were exposed, ren-
dered it very desirable to control their indications by an indepen-
dent method." Again, at page 299, we find : — " I ou^ht to men-
tion that in taking the bottom temperature with the Six's thermo-
meter the instrument simply indicates the lowest temperature to
which it has been subjected; so that if the bottom water were
warmer tlum any other stratum through which the thermometer
had paased^ the observations would be erroneous." Undoubtedly
this would be the case in extreme latitudes, or in any spot where
the temperatiu*e of the air is colder than that of the ocean*
Ge^rtainly ttie instrument might be warmed previous to lowering ;
but if tbi c^^t water should bQ on the sur&ce, no reading, to be
depended oppn, could be obtained.
It wfl« on reading these passages in the book above referred to
that it beaame a matter (^ serious consideration with us wheth^ a
xa
Digitized by VjOOQ IC
308
Royal Sociefy : —
thermometer could be constructed which could not possibly be put
out of order in travelling or by incautious handling, and which
should be above suspicion and perfectly trustworthy in ite indica-
tions. This was no very easy task. But the
instrument now submitted to the Fellows of the
Boyal Society seems to us to fulfil the above
onerous conditions, being constructed on a plan
different from that of any other self-register-
ing thermometers, and containing as it does
nothing but mercury, neither alcohol, air, nor
indices. Its construction is most novel, and
may be said to overthrow our previous ideas of
handling delicate instruments, inasmuch as its
indications are only given by upsetting the in-
strument. Having said this much, it will not
be very difficult to guess the action of the ther-
mometer ; for it is by upsetting or throwing out
the mercury from the indicating column into a
reservoir at a particular moment and in a par-
ticular spot that we obtain a correct reading of
the temperature at that moment and in that
spot. Ymt of all it must be observed that this
instrument has a protected bulb, in order to
resist pressure. This protected bulb is on the
principle devised by us some sixteen years since,
when we supplied a considerable number of ther-
mometers thus protected to the Meteorological
Department of the Board of Trade ; and they
are described by the late Admiral EitsBoy in
the first Number of the * Meteorological Papers,*
page 55, published July 5th, 1857. Beferriiig
to the erroneous readings of all thermometers,
consequent on their delicate bulbs being com-
pressed by the great pressure of the ocean, he
says: — "With a view to obviate this failing,
Messrs. Negretti and Zambra undertook to make
a case for the weak bulbs, which should trans-
mit temperature, but resist pressure. Accord-
ingly a tube of thick glass is sealed outside the
delicate bulb, between which and the casing is a
space all round, which is nearly filled with mer-
cury. The small space not so filled is a vacuum,
into which the mercury can be expanded, or
forced by heat or mechanical compression, with-
out doing injury to or even compressing the
inner or much more delicate bulb:^
The thermometers now in use in the * Chal-
lenger' Expedition are on this principle, the only
difference being that the protecting chamber has
Digitized by VjOOQ IC
Messrs. Negretti andZamhrtk on a Deqhsea Thermometer. 809
been partly filled with alcohol instead of with mercury ; but that
has nothing to do with the principle of the iavention.
We have therefore a protected bulb thermometer, like a siphon
with parallel le^, aU in one piece, and haying a continuous com-
munication, as in the annexed figure. The s^e of this thermo-
meter is pivoted on a centre, and, being attached in a perpendi-
cular position to a simple apparatus (which will be presenfly de-
scribed), is lowered to any depth that may be desu*ed. In its
descent the thermometer acts as an ordinary instrument, the mer^
cury rising or &lling according to the temperature of the stratum
through which it passes ; but so soon as the descent ceases, and
a reverse motion is given to the line, so as to pull the thermometer
to the B\irface, the instrument turns once on its centre, first bulb
uppermost, and afterwards bulb downwards. This causes the
mercury, which was in the left-hand column, first to pass into
the dilated siphon bend at the top, and thence into the nght-hand
tube, where it remains, indicating on a graduated scale the exact
temperature at the time it was tunied over. The woodcut shows the
position of the mercury after the instrument has been thus turned on '
its centre. A is the bulb ; B the outer coating or protecting cy-
linder ; G is the space of rarefied air, which is reduced if the outer
casing be compressed ; D is a small glass plug on the principle of
our Patent Maximum Thermometer, which cuts off, m the mo^
ment of turning, the mercury in the column from that of the
bulb in the tube, thereby ensuring that none but the mercury in
the tube can be transferred into the indicating column ; E is an
enlargement made in the bend so as to enable the mercury to pass
quickly from one tube to another in revolving ; and F is the indi-
cating tube, or thermometer proper. In its action, as soon as
the thermometer is put in motion, and immediately the tube has
acquired a sb'ghtly oolique position, the mercury breaks^off at the
pomt D, runs into the curved and enlarged portion E, and even-
tually f aUs into the tube F, when this tube resumes its original
perpendicular position.
The contrivance for turning the thermometer over may be de-
scribed as a short length of wood or metal having attached to it a
small rudder or fan ; this fan is placed on a pivot in connexion
with a second, and on this second pivot is fixed the thermometer.
The fan or rudder points upwards in its descent through the water,
and necessarily reverses its position in ascending. This simple
motion or half turn of the rudder gives a whole turn to the ther-
mometer, and has been found very effective.
Yarious other methods may be used for turning the thermo-
meter, such as a simple pulley with a weight which might be released
on touching the bottom, or a small vertical propeller which would
revolve in passing through the water.
Digitized by VjOOQ IC
810 a$ohgkal BoeUty :^
UOLMIOAI SOOIKT*
[Contiaued from p. 230 J
Dooembmr 17tli, ld73^~Pro£ BotuMiyi F.BA, T^oe-Preildetitj
indieChair*
The fbllowing commonioatioiui were read : —
1. ** Observationfl on some features in the Physical QwAojtf of tho
Outer Himalayan r^on of the Upper Punj&h, India.'' By A. B.
Wynne, Esq., F.G.8.
The district of the Upper PunjAb described by the anther con-
sists of crystalline, granitoid, syenitic, and schistose rocks far in
among the hills, succeeded by slates and limestones, possibly of
Silurian age, unconformably overlain by Triassic and perhaps older
iDcks, which are in their turn unconformably succeeded by a series
of mutually conformable Jurassic, cretaceous, and nummuutic lime-
stones and shaly beds. These secondary and Tertiary beds, which are
. chiefly limestones, are called the ** Hill Limestones." Beyond these
comes a zone of hiUs and broken plains, composed of sandstones, clays,
and conglomerates, of great thickness and of Tertiary age (Eocene
and Miocene), which the author calls the '' Murree beds.*' Thia belt
passes generally along the whole southern foot of the Himalayas,
from Assam to AfghanisUin. In the district described by the
author it is bounded on the south by the Salt Bange, beyond which
stretch tho deserts of the Punjftb and Sind.
The outer Tertiary belt presents a gradation towards the hill
character. Among the rocks of the Murree zone there are harder
beds than elsewhere; limestones occasionally appear, sometimes
like those of the hiU-beds, and the Hill Nummulitic limestones may
have alternated in their upper part with the Murree beds. The
nummulitic limestones of the Salt Bange, containing large Bitalven
and Gasteropoda, were probably of shallow*water origin, whilst the
diminutire organisms of the Hill Nummulitic limestone inhabited
greater depths.
Contortion of the strata is a common feature of the country,
affectmg some of the newest Tertiary beds so as to place them in a
vertical position, and almost everywhere throwing the rocks into
folds, producing in many ca^es invendons of the strata.
The author compares these rocks with those of the Simla area
described by Mr. Medlicott, who found there two strong imoon-
formities, namely, between his Siwa^ik and Kalum, and Nalum and
Subathu groups, and rejarded the whole of the beds of the outer
Tertiary detrital 2one from the base of the Subathu group upwards
as discordant to the Himalayan or'Hill-series and to each o^er.
The junction of the newer Tertiaries with the rocks forming the
higher hills of the outer Himalaya, both In the Simla area and in the
outer Punj&b, is marked by disturbance, distortion, and inversion or
abnormal superposition in the Tertiary strata along the contact.
Digitized by VjOOQ IC
Mode of Ocenmnoi qfDianwndt in South Africa* 811
In iha Upper Ftmjftb the jutustton Mbws a curred Hm^ raudng^
nenrhr east sad wesi to the nort^ of Banml Pindee ; than de«
•erimiig aa an|^ whidi doeelf fottows the great bend of the Jhilam
virer near Kocnfferabad, it rana more or less in a sontii-eaaterly
direetkm through Kashmere towards Simla. Thia Jtmction Ihie is
inaeparaldy eonneeted with the eauaation of the great mountain-'
ehama ; it ahowa a panlleliam to the axes of the outer ranges, and
is Mety due to intensity of disturbance^ the result of bteral
pressure*
The author also refers to the difference existing between the
geology ol the outer Himalayan region and that of &e Salt Bange,
as bong similar to tiiat wliioh obtains between the Alpine and
extra- Alpine diaraeters of Eur(n>ean nx^-groups, and suggests that
the recurrence of such similar features at such distances may indi-
eate a connexion between the former eonditions of deposition and
the early history of the great chains themselres.
2. '' On the mode of occurrence of Diamonds in South Africa.'^
By E. J. Dunn^ Esq. Communicated by Prof. Bamsay, FJEU3.«
T.P.G.S.
In this paper the author stated that the diamonds of South AMca
occur in peculiar circular areai^ which he regards as <* pipes,'' which
formerly constituted the connexion between molten matter below
and surfece Yolcanoes. The surrounding country counts of horizontal
shales, through which these pipes ascend nearly yertically, bending
upwards the edges of the shales at the contact. The rock occupying
uese pipes was regarded by the author as probably Gabbro, al«
thon^ in a yery altered condition. Intercalated between the 8hale«
beds there are sheets of dolerite <&o. ; and dykes of the same rocks
also intersect the shales at firequent intervals. "Within the pipes
tiiere are unaltered nodules of the same dolerite. With regard to
the relation of Ihe diamonds to the rock of the ^ipes in which they
are found, tiie author stated that he thought it probable that the
latter was only the agent in bringing them to the surface, a large
proportion of the diamonds found consisting of fragments. At
the same time he remarked that each pipe furmshed diamonds of a
different character fh>m those found in other pipes.
Jannaiy 7th, 1874.— Prof. Bamsay, Y£XJA^ Yioa-Pie«dent,
in the Chair.
The following communications were read : —
1. " The Origin of some of the Lake-basins of Cumberland.'*
— First Paper. By J. Clifton Ward, Esq., P.G.S., Assoc. E.S.M.
After rearing to the fkct that the question of the origin of lake-
basins cannot be satisfactorily discussed unless the depth of the
lakes and the heights of the mountains are brought before the
ndnd'is eye in their natural proportions, the author sketched out the
physical geography of the lakes under discussion (Perwentwatery
Digitized by VjOOQ IC
312 GeohffuuU Society: —
Bassenthwaite^ Buttennere, Gnunmooky and Loweswater), and
pointed out what must have beeft their original edse and shape
before they were filled up to the extent they now are. These lakes
were not moraine-dammed^ but true rock-basins. The belief that
the present Lake-district scenery ^was the result of the sculpturing
of atmospheric powers, such as we see now in operation, varied by
dimatal changes and dianges in the height of the district above the
sea, was enforced, and the opinion given that the work of elabora^
tion of the lake-country scenery has been going on ever since Gar-
boniferous or pre-Carboniferous times. The lake-hollows repre-
sented almost the last rock-shavings removed by Nature's tools.
What were the special tools producing these hollows ? Th^re being
no evidence of ^eir production by marine action or by running
water, since they do not lie in syndin^ troughs, nor along lines of
Assuring and faulting, and cannot be supposed to be speciid areas of
depression, it remained to see how far Professor Eunsay's. theory
accounted for their origin. The oourse of the old Borrowdale
glacier was then fully traced out, and the power the numerous
tributary glaciers had of helping to urge on the ice over the long
extent of flat ground from Seathwaite to the lower end of Bsssen-
thwaite Lake, commented on. . The same was done with regard to
the Bultermere and Lreton glacier, and the depths of the lakes,
width and form of the valleys, and thickness of the ice shown by
numerous transverse and longitudinal sections drawn to scale.
When all the evidence was considered — the fact of the lake-hoUows
under examination being but long shallow troughs, the thickness
of the ice which moved along the valleys in which the lakes now
lie, the agreement of the deepest parts of the lakes with the points
at which, from the confluence of several ice-streams and the nar-
rowing of the valley, the onward pressure of the ice must have been
greatest — the conclusion was arrived at that Prof. Bamsay's theory
was fully supported by these cases, and that the immediate cause of
the present lake-basins was the onward movement of the old
glaciers, ploughing up their beds to this slight depth. It was
pointed out dat since the general form of tiie Buttermere and
Grummock valley was that of a round-bottomed basin, as seen in
transverse section, the effect of the ice was merely a slight deepen-
ing of the basin or the formation of a smaller basin of similar
form at the bottom of the larger ; whereiis in the case of the Der-
wentwater and Bassenthwaite valley, which in transverse section
was a wide flat-bottomed pan, the action was to form long shallow
grooves at the bottom of the pan. This consideration was thought
to explain the fact of the greater depth of Buttermere and C^m-
mock than of Derwentwater and Bassenthwaite, although the size and
thickness of the old glacier in the former case was probably less
than in the latter. Li conclusion, the author stated that he hoped
to test the results obtained in these cases by bringing forward in a
foture paper like details of Wastwater and other lakes and moun-
tains in the district.
Digitized by VjOOQ IC
On a great Ice-sKeet in this Lake^dktrUt. 818
2. << On the Traces of a Great loe-sheet in the Sonthem part of
the Lake-district and in North WaleeJ'' By D. Maddntoeh, Esq..
P.G.S.
In this pap^r the author brought forward the eyidence which
seems to him to establish the existence in the sonthem part of the
Lake*district of a *< valley-ignoring and ridge-concealing ice-sheef
With regard to ice-marks, he distingnished between primary strias
and those produced at a subsequent period, and stated that in the
Lake-district the direction of the primary strife generally coincides
with that of the action by which nKhes mou^onneM have been pro-
duced. He gave a table of the direction of ice-marks observed by
him in the district under notice, and stated that about Windermere
and Ambleside the general direction is nearly N.N.W., round Gras-
mere between N.W. and N.N.W., north-west and west of Grasmei^
in upland valleys and on high ridges about N. 30^ W., south of Gras-
mere and in Great Langdala N. 35^ W., and in the Coniston district
a little W. of N. In many places he recognized an uphill march of
the ice. He thought that the iceflow producing these marks
might be anterior to the flow from south to north, of which traces
are observed in the northern part of the Lake-district, and that
its source was probably a vast mass of ice covering many square
miles of country north of Far Easdale. The author also referred to
the glaciation of North Wales, some of the marks of which, observed
by him in a district south of Snowdon, seemed to him to indicate the
southerly movement of a great ice-sheet capable of ignoring or
crossing deep valleys. He noticed that towards the top of the pass
of lianberis there is a thin covering of drift on the 8.W. side,
resembling the gravelly pinnel of the Lake-district. He also men-
tioned the occurrence near Llyn Ilydan of numerous mounds
composed of clay, sand, and fine gravel, the stones having generally
been rolled by water, and ascribed their formation to a combination
of glacial and marine actions.
8. '< Notes on some Lamellibrandis from the Budleigh-Saltcrton
Pebbles.*' By Arthur Wyatt Edgell, Esq., F.G.8.
In this paper the author commenced by noticing the accordance
between many of the pebbles of Budleigh Salterton and beds occur-
ring on the opposite side of the channel in Brittany, and then de-
scribed several species of Lamellibranchiata found in the Budleigh-
Salterton pebbles. The species described were : — ModiolopsU ar-
morioi (Salter), M. Lebeseontiy sp. n., Sangumalites ?, sp. (contartus ?,
Salter), Avieulopecien Tromelini^ sp. n., Fterinasa retrofleaa (Hi-
singer) and three other species, Pdlcearca, sp.^ Avicula, sp., Okido^
pTwrw?, sp., Lunvloeardvum ventricomtni sp. n., CkfMdonta^ sp., and
Digitized by VjOOQ IC
C 81* ]
XLY. InielSgenoi and MUeithneoui Artklm.
ON THE ACTION OF TWO SLBMENTt Of A CU&&1NT.
BT jr. BBBTAAND.
««rnwO p«nM owrents ftttnoi one isotiier when tbej ]mm iba
are oppoeite^" After enunfliatnig this rule, Ampiae beliered hm
could immediatelj ^^lenJiae it bj extending it to the elemantt of
the correntfl^ to which he i^plm^ wheterer nuij be thcdr rdaim
direction, the ide* of a coune in the latne or in opposite directicns^
Two currenis ue Mid to be in the aame direction iriien they boUi
increaBC their distance from the foot of the common perpendiciihr»
oar when thej both approach it; in the contruy cases thejr hare
di&rent directions. Adoptang this kngoage, it is not aocozate to
sav that two elements haying the same diroction attract one the
other; it is not accurate eren for parallel elements. As theasser*
tion l»s been reprodnced in all the treatises on^jsics, and senrea
as a basis for sereral important e^lanations, I haye thought it
would be important to show tiiat it is inconsistent with Ampere's
law itself, and to solve the following problem : —
GKyen an element oi a current, to nnd in a point M of space tte
diredion whidi must be assigned to another ekmeiit in order that
thttr mutual action may be attractire, repellent, or nil.
Suppose the dement d* placed at the origin of the ooordinateB
and diiected along the axis of the X's, let us seek the condition on
whidi an element whose coordinates are ^, y', 2^ will be without
acti<mon<2f. Namina the angles formed by the two elements inth
the straight line which joins them d and a , and ihe an^ which
they make with one anouier «, according to the law of Ampere the
condition is,
cose=|cosdcos^ (l)
But, naming the radius yector 1*, and the atbiMsting element ds', we
haye
^ af ^ dr dad
COSe«-, COSa^acTj, COSCB^.
Equation (1) becomes
r
^ ""U
of which the integnd is
i^^hji^, (3)
the equation of a sur&ce of reyolution wh